Answer:
35 units
Step-by-step explanation:
Dr.Osborne has scheduled Anita Blanchette for a spirometry test and wants you to telephone her the day before the test to prepare her so that optimal results are obtained.
1.) What information do you give Anita before her spirometry so that the best test results can be obtained?
2.) How would you explain the rationale for the performance of this procedure?
To ensure the best test results, Anita should be provided with the following information before her spirometry:
1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.
2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.
3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.
4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.
The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.
Learn more about spirometry and its significance in assessing lung function:
https://brainly.com/question/18155241
#SPJ11
how to partition a line segment with a given ratio
To partition a line segment with a given ratio, you can follow these steps:
1. Identify the two endpoints of the line segment. Let's call them point A and point B.
2. Determine the ratio in which you want to partition the line segment. For example, let's say the ratio is 2:1.
3. Use the ratio to divide the line segment into parts. To do this, you'll need to find a point, let's call it point C, that is a certain distance from point A and a certain distance from point B. The distance from point A to point C should be twice the distance from point C to point B.
4. To find point C, calculate the total length of the line segment by finding the distance between point A and point B. Let's say the length of the line segment is d.
5. Divide d by the sum of the ratio (2+1=3) to determine the length of each part. In this case, each part would be d/3.
6. Multiply the length of each part by the corresponding ratio factor to determine the distance from point A to point C. In this case, point C would be located at a distance of (2/3) * (d/3) from point A.
7. Similarly, multiply the length of each part by the remaining ratio factor to determine the distance from point C to point B. In this case, point C would be located at a distance of (1/3) * (d/3) from point B.
8. Once you have the coordinates of point C, you have successfully partitioned the line segment with the given ratio.
For example, let's say the line segment AB has a length of 12 units and we want to partition it with a ratio of 2:1. Using the steps above:
1. Identify the endpoints: A and B.
2. Ratio: 2:1.
3. Calculate each part: d/3 = 12/3 = 4 units.
4. Distance from A to C: (2/3) * (d/3) = (2/3) * 4 = 8/3 units.
5. Distance from C to B: (1/3) * (d/3) = (1/3) * 4 = 4/3 units.
6. Point C would be located at coordinates (8/3, 4/3) on the line segment AB.
Remember, these steps can be modified based on the specific ratio you are given.
to know more about line segments here:
brainly.com/question/25727583
#SPJ11
Question- Partitioning a line segment, AB, into a ratio a/b involves dividing the line segment into a + b equal parts and finding a point that is an equal part from A and b equal parts from B. When finding a point, P, to partition a line segment, AB, into the ratio a/b, we first find a ratio c = a / (a + b)
4. Write the following quadratics as products of two binomials. f(x) = 6x2 + 66x + 60
Answer:
f(x)=(6x+6)(x+10)
Explanation:
Given the quadratic expression:
\(f\mleft(x\mright)=6x^2+66x+60\)First, we can rewrite it in the form below:
\(f\mleft(x\mright)=6x^2+60x+6x+60\)Next, factor the terms:
\(\begin{gathered} f(x)=6x(x+10)+6(x+10) \\ \implies f(x)=(6x+6)(x+10) \end{gathered}\)Thus, the quadratics as a product of two binomials is:
\(f(x)=(6x+6)(x+10)\)What is the value of x?
Enter your answer in the box.
x =
Answer:
39°
Step-by-step explanation:
To answer this question it's important to remember that all triangles have 3 angles which sum to 180. This means that we can set up an equation to find the missing angle
Create the equation
\(39+102+x=180\)Combine like terms
\(141+x=180\)Subtract 141 from both sides
\(x=39\)This means that the missing angle is 39 degrees. Since two of the angles are equal to 39, this also means that this triangle is isosceles.
which time-series model assumes that demand in the next period will be equal to the most recent period’s demand? A) Naïve approach
B) Exponential smoothing approach
C) Moving average approach
The time-series model that assumes that demand in the next period will be equal to the most recent period's demand is A) Naive approach.
What is Naïve approach model?This model is based on the simplest assumption of all, that the next period's demand will be equal to the current period's demand. It is called the naive approach because it assumes no underlying pattern in the data and provides a baseline prediction. The formula for the naive approach is as follows:
y(t) = y(t-1) where y(t) represents the demand in period t and y(t-1) represents the demand in the previous period.
Although this model is simple, it is often used as a benchmark for comparison with more complex models and can provide reasonable results for stable demand patterns.
Learn more about time-series model here:
brainly.com/question/15114845
#SPJ4
neil recorded the amount of rain that fell over the coures of three days in april. on day one he recorded 1.25 . on day 2 he recorded 0.7
It can be expect approximately 7.61 inches of rain for the rest of the month of April.
To determine how much more rain can be expected for the rest of the month, we need to calculate the total rainfall recorded for the three days and subtract it from the average rainfall for April.
The total rainfall recorded for the three days is:
1.25" + 0.7" + 3.09" = 5.04"
The average rainfall for April is given as 12.65".
To find how much more rain can be expected for the rest of the month, we subtract the total recorded rainfall from the average rainfall:
12.65" - 5.04" = 7.61"
Therefore, you can expect approximately 7.61 inches of rain for the rest of the month of April.
Learn more about average here:
https://brainly.com/question/24057012
#SPJ11
The correct question is:
Neil recorded the amount of rain that fell over the course of 3 days in April on one day he recorded 1.25" on day 2 he recorded 0.7" and on day 3 he recorded 3.09" the average rainfall for April is 12.65" how much more rain can you expect this month?
What percent of 108 is 33?
Can someone help Ive tried doing this but I don’t understand it. The answer sheet says it’s supposed to be 30.6% but I keep getting 32.67%
Answer:
30.6%, see explanation for what you're asking for
Step-by-step explanation:
Set up a proportion equation. You know 108 is 100%, so keeping the percents on the top, 100%/108 = x%/33. There's no "nice" number multipliers here, but you can still divide 100 by 108, take that number, and multiply it by 33 to get x. This is because you're finding how to get from 108 to 100 (bottom to top) to see that proportion, then applying it to the bottom number under x, the top, which you want. Doing this gives me 0.936 (approx.), and multiplying this by 33 gives me 30.555 repeating, which can be rounded up to 30.6%.
I can't figure out why you're getting a number like 32.67%. Perhaps it's a rounding error? I hope this helps despite it being a week after your asking.
In the figure, mZEDF = 42°. Which other angle must have the same measure?
D
420
AEGF
B. ZGDF
C. ZEGD
D. ZDEG
E
Answer:
A
Step-by-step explanation:
angles on the circle (inscribed angles ) from the same arc are congruent.
∠ EDF and ∠ EGF are formed by the same arc EF and are congruent
∠ EGF ≅ ∠ EDF
Of the 16 students in the school orchestra, 12.5 % play the violin. How many students in the orchestra play the violin?
Answer:
2
Step-by-step explanation:
16 -> .16
.16×12.5=2
You just move the decimal point 2 times and multiply by the percentage
Answer:
2 students
Step-by-step explanation:
12.5% = 0.125
Multiply this by 16:
16 * 0.125 = 2
Compute revenue and variable costs for each show Use the equation approach to compute the number of shows Tower Productions must perform each year to break even. Use the contribution margin ratio approach to compute the number of shows needed each year to earn a profit of $4,128,000. Is this profit goal realistic? Give your reasoning. Prepare Tower Productions's contribution margin income statement for 140 shows performed in 2018. Report only two categories of costs: variable and fixed 3. 4. Tower Productions performs London shows. The average show sells 900 tickets at $65 per ticket. There are 140 shows per year. No additional shows can be held as the theater is also used by other production companies. The average show has a cast of 55, each earning a net average of $330 per show. The cast is paid after each show. The other variable cost is a program-printing cost of $9 per guest. Annual fixed costs total $580,500. Read the requirements Requirement 1. Compute revenue and variable costs for each show. Select the formula and enter the amounts to compute sales revenue for each show. = Sales revenue per show Select the formula and enter the amounts to compute variable costs for each show. Compute the variable costs per show for each cost separately, and then compute the total variable costs per show. Variable costs per show Cost of programs Cost of performers Total variable costs Requirement 2. Use the equation approach to compute the number of shows Tower Productions must perform each year to break even First, select the formula to compute the required sales in units to break even. Target profit Rearrange the formula you determined above and compute the required number of shows to break even The number of shows needed annually to break even is Requirement 3. Use the contribution margin ratio approach to compute the number of shows needed each year to earn a profit of $4,128,000. Is this profit goal realistic? Give your reasoning. Begin by showing the formula and then entering the amounts to calculate the required sales dollars to earn a profit of $4,128,000. (Round the required sales in dollars to the nearest whole dollar. Round amounts in the formula to two decimal places, XX.XX. Abbreviation used: CM contribution margin.) Required sales in dollars - )1 Now use the information given and the required sales in dollars computed in the previous step to determine the required number of shows needed each year to earn a profit of $4,128,000. (Round your answer up to the nearest whole number.) The number of shows needed annually to earn a profit of $4,128,000 is Is this profit goal realistic? Give your reasoning.
Tower Productions would need to perform approximately 128 shows each year to earn a profit of $4,128,000.
To answer the given requirements, we need to calculate the revenue and variable costs for each show, determine the number of shows needed to break even using the equation approach, calculate the number of shows needed to earn a profit of $4,128,000 using the contribution margin ratio approach, and evaluate if the profit goal is realistic.
Let's calculate each step:
Requirement 1:
Revenue per show = Average tickets sold per show * Ticket price
Revenue per show = 900 * $65 = $58,500
Variable costs per show:
Cost of programs = $9 per guest * 900 guests = $8,100
Cost of performers = Number of performers * Net pay per show
Cost of performers = 55 * $330 = $18,150
Total variable costs per show = Cost of programs + Cost of performers
Total variable costs per show = $8,100 + $18,150 = $26,250
Requirement 2:
To compute the number of shows Tower Productions must perform each year to break even, we use the equation approach:
Break-even sales in dollars = Fixed costs + Target profit
Break-even sales in dollars = $580,500 + $0 (since it's break-even)
Number of shows needed to break even = Break-even sales in dollars / Revenue per show
Number of shows needed to break even = $580,500 / $58,500 = 9.93
Therefore, Tower Productions must perform 10 shows each year to break even (rounded up to the nearest whole number).
Requirement 3:
To compute the number of shows needed each year to earn a profit of $4,128,000 using the contribution margin ratio approach:
Contribution margin ratio = (Revenue per show - Total variable costs per show) / Revenue per show
Contribution margin ratio = ($58,500 - $26,250) / $58,500 ≈ 0.552
Required sales in dollars = Target profit / Contribution margin ratio
Required sales in dollars = $4,128,000 / 0.552 ≈ $7,476,403.63
Number of shows needed to earn a profit of $4,128,000 = Required sales in dollars / Revenue per show
Number of shows needed to earn a profit of $4,128,000 = $7,476,403.63 / $58,500 ≈ 128
Therefore, Tower Productions would need to perform approximately 128 shows each year to earn a profit of $4,128,000.
Based on the given information and calculations, it is difficult to determine if the profit goal of $4,128,000 is realistic without additional context or industry benchmarks. It would require careful evaluation of various factors such as market demand, competition, and historical performance. Additionally, it would be important to consider whether the theater's capacity and scheduling constraints allow for a sufficient number of shows to achieve the desired profit.
To learn more about profit click here:
brainly.com/question/16857789
#SPJ11
(please help)!!!!!!!!!!!!!!
Answer
use trigonometry to find both the answers.
i have done the working out in the picture hope it helps...
Step-by-step explanation:
4(y – 6) = –4 I need help
Answer:
y=5
Step-by-step explanation:
4(y-6)=-4
4y-24=-4
+24 +24
4y=20
y=5
Sam has 16 pounds of cat food is going to separate it into 1/4 pound portions. How many portions of cat food will he have
Answer:
Sam will have 4 portions. In those 4 portion will be 4 pounds per portion because 16 divide 4 Is 4
uh someone help with this question -photo attached-
Answer:
c)-2 is greater than -6
Step-by-step explanation:
When f(x) = -3, what is x?
Answer:
not enough info
Step-by-step explanation:
f times x equals -3 there could be many answers like f is 1 x is -3 or f is -3 x is 1 and more
2-yard piece of ribbon costs $1.26. What is the price per foot?
1 yard = 3 feet
3ft * 2 yards = 6 feet
$1.26 / 6ft = $0.21 / ft
3. Calculate the initial velocity of the ball using the formula V=V+ agt.Use -9.8m/s2
for ag.
4. Solve for the maximum height reached by the ball using h=vit + 1⁄2 agt. Use -9.8m/s2 for ag.
TABLE 4. Data on the Velocity of the Ball and Height of the Building
Trial
Velocity, v(s)
Height, h (m)
1
2
3
Average
Guide Question:
Q 9. What will happen to the ball's velocity as it falls further below the point
of release?
As the ball falls further below the point of release, its velocity increases in magnitude due to the acceleration of gravity. The initial velocity (V0) at the point of release remains constant, while the time (t) increases.
As the ball falls further below the point of release, its velocity will increase in magnitude. The ball experiences acceleration due to gravity (ag) acting in the downward direction.
In the given formula V = V0 + agt, the initial velocity (V0) represents the velocity of the ball at the point of release. Since the velocity of the ball is positive when it is released, we can assume the initial velocity (V0) is positive.
As the ball falls, the acceleration due to gravity (ag) remains constant at -9.8 m/s^2 (negative sign indicates the downward direction). The value of t represents the time elapsed since the ball was released.
In the formula h = V0t + (1/2)agt, the height (h) represents the vertical distance traveled by the ball. The initial velocity (V0) and the acceleration due to gravity (ag) have the same signs (both negative or both positive) because they act in the same direction during the ball's motion.
As the ball falls further below the point of release, the value of t increases. Therefore, the term V0t in the equation becomes larger, contributing to the increase in the height reached by the ball.
For more such question on acceleration of gravity visit:
https://brainly.com/question/29037259
#SPJ8
X
y
1
9
2
7
3₂
3
6
4
7
1 -2
a. Graph the points above as a scatter plot.
b. Calculate the correlation coefficient.
8
-5
10
-8
10
X is top y is bottom
The correlation coefficient of points is a negative correlation.
The given coordinates are (1, 9), (2, 7), (3, 6), (4, 1), (7, -2),(8, -5) and (10, -8).
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
• A scatter plot with increasing values of both variables can be said to have a positive correlation.
• A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.
The given coordinate points are plotted on graph.
From the graph (scatter plot) we can see that, the points have a negative correlation.
Therefore, the correlation coefficient of points is a negative correlation.
To learn more about the scatter plot visit:
https://brainly.com/question/29231735.
#SPJ1
what is the probability that a standard normal random variable will be between .3 and 3.2?
According to the z table, there is a 0.3814 percent chance that such a standard normal random variable would fall between 0.3 and 3.2.
What is the probability?
The possibility of an event occurring is stated as a number between 0 and 1, where 0 indicates that the event cannot occur and 1 indicates that the event is guaranteed to occur. The probability of an event A is defined mathematically as the number of positive outcomes divided by the total number of alternative outcomes.
We must determine the likelihood that a standard normal random variable would occur with a probability between 0.3 and 3.2.
First, a standard normal random variable with a mean and standard deviation is introduced.
We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.
The probability therefore should be
P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)
Using z's typical value
P(0.3<z<3.2)=0.9993−0.6179
P(0.3<z<3.2)=0.3814
Therefore, there is a 0.3814 percent chance that a standard normal random variable would fall between 0.3 and 3.2.
To know more about standard normal random variable visit:
brainly.com/question/14782203
#SPJ4
What’s the answer to this?!!!!
Yes, it is a right triangle.
Answer:
Yes
Step-by-step explanation:
Yehvsbsgwbdhgjebwjosnwks
/_AGB and /_EGD are angles
The angle ∠AGB and ∠EGD are equal angles / opposite angles / vertical angles.
Given,
∠AGB and ∠EGD
We need to find what types of angles are ∠AGB and ∠EGD.
What are vertical angles?Vertical angles are angles that are opposite of each other when two lines cross.
Vertical angles are always equal.
We have,
∠AGB and ∠EGD are vertical angles
∠AGB = 30 = ∠EGD
∠CGD and ∠AGF are vertical angles.
∠CGD = 50 = ∠AGF
∠BGC and ∠FGE are vertical angles.
∠BGC = ∠FGE = 2x
We know that,
A straight angle is 180.
∠FGC =180
∠FGC = ∠AGF + ∠AGB + ∠BGC
180 = 50 + 30 + ∠BGC
180 - 50 - 30 = ∠BGC
180 - 80 = ∠BGC
∠BGC = 100
∠FGE = 100
We also see that,
∠FGC = ∠FGE + ∠EGD + ∠CGD
180 = 100 + ∠EGD + 50
180 - 150 = ∠EGD
∠EGD = 30
We see that,
∠EGD = 30°
∠AGB = 30°
Thus, the angle ∠AGB and ∠EGD are equal angles / opposite angles / vertical angles.
Learn more about Vertical angles here:
https://brainly.com/question/24460838
#SPJ1
1) y = 7x+12
y=-8x-3 I need this step by step I don’t understand
Answer: x=-1, y=5
Step-by-step explanation:
First, 7x+12 is substituted in for y in the second equation
7x+12=-8x-3
Add 8x to both sides
15x+12=-3
Subtract 12 from both sides
15x=-15
Divide both sides by 15
x=-1
To solve for y, substitute x into the first equation
7(-1)+12=y
-7+12=y
5=y
Algebra 1
> U.15 Solve a system of equations using any method: word problems GDQ
Tutor
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks
Victor and Susan each want to run for president of their school's student body council. In
order to do so, they must collect a certain number of signatures and get a nomination. So far,
Victor has 23 signatures, and Susan has 19. Victor is collecting signatures at an average rate
of 9 per day, whereas Susan is averaging 11 signatures every day. Assuming that their rate of
collection stays the same, eventually the two will have collected the same number of
signatures. How long will that take? How many signatures will they both have?
In
days, Victor and Susan will each have collected
signatures.
Submit
O
к
Answer:
cl jsjsjsjnsmamansnsnannananann
I need the answer pleasee 9.5 In an effort to determine the relationship between annual wages, in 000,for employ ees and the number of days absent from work because of sickness,a large corporation studied the personnel records for a random sample of 12 employees.The paired data are provided below: Employee Annualwages('000) Days missed 1 25.7 4 2 27.2 3 3 23.8 6 4 34.2 5 5 25.0 3 6 22.7 12 7 23.8 5 8 28.7 1 6 20.8 12 10 21.8 11 11 35.4 2 12 27.2 4 Determine the correlation cocfficicnt and test to see whether thc number of days missed is related to annual wages,at the 5 per cent level of significance. If it is,find the regression equation for predicting the number of likely absence in days. Interpret its coefficients and use it to predict the likely absence of an employee earning f25,000
First, let's calculate the correlation coefficient: Using the given data, we find that the correlation coefficient (r) is approximately -0.625.
To test the significance of the relationship, we can perform a hypothesis test using the t-test. At the 5% level of significance, with 10 degrees of freedom, the critical t-value is approximately 2.228.
Since the calculated t-value (-2.430) is greater than the critical t-value, we can reject the null hypothesis and conclude that there is a significant relationship between the number of days missed and annual wages.
Next, to find the regression equation, we can use the method of least squares. The regression equation for predicting the number of likely absences in days is:
Days Missed = -2.285 + 0.334 * Annual Wages
The coefficient -2.285 represents the intercept of the regression line, and the coefficient 0.334 represents the slope, indicating the change in the number of days missed for each unit increase in annual wages.
To predict the likely absence of an employee earning $25,000, we substitute the value into the regression equation:
Days Missed = -2.285 + 0.334 * 25 = 5.84 (approximately)
Therefore, it is predicted that an employee earning $25,000 is likely to be absent for approximately 5.84 days.
Note: The interpretation of the coefficients depends on the context of the data and the units used for annual wages and days missed.
To learn more about Regression line - brainly.com/question/29753986
#SPJ11
Point Q'(3, 2) is the image of Q(6, 4) under a translation. Determine the translation. Use non-negative numbers. A translation by up/down units to the right/left v and units
A translation by 3 units to the left and 2 units down.
Given points are:-
Q' = (3, 2) ; Q = (6, 4)
As Q' is the image of Q under translation,
The translation is from (6, 4) to (3, 2).
That is the values (h, k) was added to the coordinates where ...
6 + h = 3
or, h = -3 ....... a translation of 3 to the left.
It means on the x-axis, the point changed from 6 to 3, which means that the point was shifted 3 units to the left.
and
4 + k = -2
or, k = -2 ....... a translation of 2 to the down.
it means that on the y-axis, the point changed from 4 to 2, which means that the point was shifted from 2 units to down.
To learn more about translation, visit: https://brainly.com/question/13787782
#SPJ9
PLEASE HELP THIS IS URGENT I WILL MARK U THE BRAINLIEST PLS HELP!!!!!
In a sale, normal prices are reduced by 20%.
Andrew bought a saddle for his horse in the sale.
The sale price of the saddle was £220.
Calculate the normal price of the saddle.
Answer:
the normal rice of saddle is £275
Step-by-step explanation:
normal prices are reduced by 20% to get sale price
this can be shown that
normal price = 100%
and sale price is 80% of normal price (100%-20%)
therefore we can use cross multiplication
% amount( £)
80 : 220
100 : x
80x = 22000
x = 22000/80
x = 275
the normal rice of saddle is £275
suppose you roll two number cubes and multiply the numbers. what is the probability of getting a multiple of 3 and 4
For given experiment, the probability of getting a multiple of 3 and 4 is 1/7
In this question we have been given an expreiment of rolling two number cubes and multiply the numbers.
We need to find the probability of getting a multiple of 3 and 4
If two number cubes are rolled and multiply the numbers, the maximum output of multiplication would be 36
So, the sample space:
n(S) = 21
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
And the multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36
The number of outcomes for getting a multiple of 3 and 4 are:
12, 24, 36
n(A) = 3
so, the required probability would be,
p(A) = n(A)/n(S)
p(A) = 3/21
p(A) = 1/7
Therefore, the probability of getting a multiple of 3 and 4 = 1/7
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
The steepness, or grade, of a highway or railroad is expressed as a percent. In the photo of the cog railway at Pike's Peak, in Colorado, the grade is 18%. Thus, for every 100 ft of horizontal run, the train rises 18 ft. Find the angle of the inclination of the railway. a. 10.2° c. 7.85° b. 15.7° d. 19.2°
Answer:
10.20°
Step-by-step explanation:
Given that:
Grade = 18% ; rise = 18ft
For every 100 feets, plane roses 18%
The question can be solved using Pythagoras rule :
Tangent θ = opposite / Adjacent
Tan θ = 18 / 100
Tan θ = 0.18
θ = tan^-1(0.18)
θ = 10.203973
θ = 10.20°
A or D im not sure if the variable should be negative.
Answer:
d
Step-by-step explanation:
give me brainlist
Answer:
The correct answer is D
How many years will it take $2,000 to grow to $3,300 if it is invested at 4.75% compounded continuously?
Answer:
10.54263764
Step-by-step explanation:
\(3300=2000e^{.0475t}\\\\1.65=e^{.0475t}\\\ln(1.65)=.0475t\\.500775288=.0475t\\t=10.54263764\)
Answer:
It will take about 10.5 years for the investment to reach $3,300.
Step-by-step explanation:
Continuous compound is given by:
\(\displaystyle A=Pe^{rt}\)
Where P is the principal, e is Euler's number, r is the rate, and t is the time (in this case in years).
Since our principal is $2,000 at a rate of 4.75% or 0.0475, our equation is:
\(\displaystyle A=2000e^{0.0475t}\)
We want to find the number of years it will take for our investment to reach $3,300. So, substitute 3300 for A and solve for t:
\(3300=2000e^{0.0475t}\)
Divide both sides by 2000:
\(\displaystyle e^{0.0475t}=\frac{33}{20}\)
We can take the natural log of both sides:
\(\displaystyle 0.0475t=\ln\left(\frac{33}{20}\right)\)
Therefore:
\(\displaystyle t=\frac{1}{0.0475}\ln\left(\frac{33}{20}\right)\approx 10.54\text{ years}\)
It will take about 10.5 years for the investment to reach $3,300.