Sunset Lake is stocked with 2800 rainbow trout and after 1 year the population has grown to 7000. Assuming logistic growth with a carrying capacity of 28000, find the growth constant kk, and determine when the population will increase to 14600.
Answers
The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.
How to find the increase of population?The increase of population can be found by using the logistic equation. It is
\(P(t) = \frac{K}{1 + Ae^{-kt} }\)
Where
P(t) = population at time t (in years)K = carrying capacityA = (K- P₀)/P₀k = growth constant of proportionalityt = time (in years)Sunset Lake is stocked with the rainbow trout. We have
P₀ = 2800P(1) = 7000K = 28000Find the growth constant k and time t when P(t) = 14600!
A = (K - P₀)/P₀
A = (28000 - 2800)/2800
A = 25200/2800
A = 9
After 1 year, we have 7000 rainbow trout. The growth constant is
\(7000 = \frac{28000}{1 + 9e^{-k(1)} }\)
\(1 + 9e^{-k} = 4\)
\(9e^{-k} = 3\)
\(e^{-k} = \frac{1}{3}\)
k = - ln (1/3)
k = 1.0986
Use k value to find the time when the population will increase to 14600!
\(14600 = \frac{28000}{1 + 9e^{-1.0986t} }\)
\(1.9178 = 1 + 9e^{-1.0986t}\)
\(0.9178 = 9e^{-1.0986t}\)
\(\frac{0.9178 }{9} = e^{-1.0986t}\)
\(t = \frac{ln \: 0.10198}{-1.0986}\)
t = 2.078
t ≈ 2.1 years
It is in another 1.1 years after t = 1.
Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.
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Related Questions
Which expression is equivalent to
(2x*y);
2
O 2x?y4
0 2412
8x?y
8x12,2
Answers
Answer:
8x?y
Step-by-step explanation:
Find a sum equivalent to 10(y + x)
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Answer: 10x + 10y
8)
Step-by-step explanation:
What is the slope of the line passing through the points (1 5/7) and (2 2/7)
Answers
Answer:
Step-by-step explanation:
\(\frac{2}{7}-\frac{5}{7} = \frac{-3}{7} \\2 - 1 = 1\\\\Hence,\\(-3/7) / 1 = -3/7\\\\Hence, slope: -3/7\)
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Algebra equation…the minimum normal glucose level for a fasting adult is 70 mg/dl. The maximum normal level is 99 mg/dl. Write an absolute value equation that represents the minimum and maximum normal glucose levels.
Answers
The absolute value equation that represents the minimum and maximum normal glucose levels is |x - 84.5| = 14.5
How to write an absolute value equation that represents the minimum and maximum normal glucose levels?The given parameters are:
Minimum = 70 mg/dL
Maximum = 99 mg/dL
Calculate the mean using:
Mean = (Minimum + Maximum)/2
This gives
Mean = (70 + 99)/2
Evaluate
Mean = 84.5
Calculate the range using
Range = Maximum -Minimum
This gives
Range = 99 - 70
Evaluate
Range = 29
The absolute value equation that represents the minimum and maximum normal glucose levels is
|x - Mean| = Range/2
So, we have:
|x - 84.5| = 29/2
Evaluate
|x - 84.5| = 14.5
Hence, the absolute value equation that represents the minimum and maximum normal glucose levels is |x - 84.5| = 14.5
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for a new customer top golf charges $10 for a player card and $2 per hour.
Answers
The cost for a new customer to rent a bay for 6 hours at Top Golf is $22, which includes a $10 player card fee and a $12 bay rental fee at $2 per hour.
Let's let "x" be the total cost for a new customer to rent a bay for 6 hours.
We know that there is a flat fee of $10 for the player card, and then an additional $2 per hour for the bay rental.
So, the equation for the cost "x" can be written as
x = 10 + 2(6)
The expression 2(6) represents the cost of the bay rental for 6 hours. We can simplify the expression by multiplying 2 and 6, which gives us
x = 10 + 12
Now, we can combine like terms to find the final cost
x = 22
Therefore, the cost for a new customer to rent a bay for 6 hours at Top Golf is $22.
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--The given question is incomplete, the complete question is given
" For a new customer top golf charges $10 for a player card and $2 per hour. Write and solve a linear equation to find the cost for a new customer to rent a bay for 6 hours."--
Triangle ABC is a 45*-45*-90* triangle where two vertices are A(-2,2) and B(-2,6) and AB is a leg of the triangle. What are all the possible ordered pairs for C?
Answers
Midpoint formula: [(x1 + x2) / 2, (y1 + y2) / 2]
For A(-2,2) and B(-2,6), the midpoint coordinates are:
C = [(-2 + -2) / 2, (2 + 6) / 2] = [-2, 4]
So, the only possible ordered pair for point C in this 45°-45°-90° triangle is (-2, 4).
A quality control manager at an auto plant measures the paint thickness on newly painted cars. A certain part that they paint has a mean thickness of 2mm with a standard deviation of 0.8mm.
The manager takes a daily random sample of thickness measurements from 100 randomly chosen points on these parts and calculates the sample mean thickness
-x from each sample. We can assume that the points in each sample are independent.
What will be the shape of the sampling distribution of -x?
Answers
Answer:
Approximately Normal
Step-by-step explanation:
Even though we don't know the shape of the population distribution of thicknesses, the sampling distribution of -x will be approximately normal since the sample size is large (n=100≥30).
chapter 8
2.Find the volume of each figure. Round your answers to the nearest hundredth, if necessary.
Answers
The volume of the given figure is 267.95 mi³.
What is the volume?The given object is a sphere. A sphere is a three-dimensional object that has all its surface points at equal distances from the center. A sphere is round in shape.
The volume of an object is the amount of space in the three-dimensional object. The radius of a sphere is a straight line from the circumference of the sphere to the center of the sphere.
Volume of a sphere = 4/3 × π × r³
Where:
π = pi = 22/7
r = radius = 4
4/3 x 22/7 x 4³ = 267.94667 mi³
267.95 mi³
To round off to the nearest hundredth, if the thousandth digit is equal to 5 or greater than 5, add 1 to the hundredth digit and change all the digits after the hundredth digit to 0.
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How do I write an equation that would allow someone to find the value of R
Answers
Answer:
R+239=3501
Step-by-step explanation:
Add the three 1,167 values together and you get 3,501. Then, because we know a portion of the three blocks is equal to 239, add it so when we solve for R, 239 is subtracted from the total.
As for solving it,
Subtract 239 on both sides, and R is 3501-239 = 3262
i dont smoke cause nobody want the smoke
Answers
Answer:
Points Yay Woop Woop
Step-by-step explanation:
Pointsssssss
Javier bought a painting for
$
150
$150dollar sign, 150. Each year, the painting's value increases by a factor of
1.15
1.151, point, 15.
Which expression gives the painting's value after
7
77 years?
Choose 1 answer:
Choose 1 answer:
(Choice A)
(
150
⋅
1.15
)
7
(150⋅1.15)
7
left parenthesis, 150, dot, 1, point, 15, right parenthesis, start superscript, 7, end superscript
A
(
150
⋅
1.15
)
7
(150⋅1.15)
7
left parenthesis, 150, dot, 1, point, 15, right parenthesis, start superscript, 7, end superscript
(Choice B)
150
⋅
1.1
5
7
150⋅1.15
7
150, dot, 1, point, 15, start superscript, 7, end superscript
B
150
⋅
1.1
5
7
150⋅1.15
7
150, dot, 1, point, 15, start superscript, 7, end superscript
(Choice C)
(
150
+
1.15
)
⋅
7
(150+1.15)⋅7left parenthesis, 150, plus, 1, point, 15, right parenthesis, dot, 7
C
(
150
+
1.15
)
⋅
7
(150+1.15)⋅7left parenthesis, 150, plus, 1, point, 15, right parenthesis, dot, 7
(Choice D)
150
+
1.15
⋅
7
150+1.15⋅7150, plus, 1, point, 15, dot, 7
D
150
+
1.15
⋅
7
150+1.15⋅7
Answers
The correct expression is \($(150 \cdot 1.15)^7$\) (Choice A).
The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).
To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.
If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.
Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.
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karla sings for 45 mins for y days each week. on the other days of the week, she plays piano for 1.5 hours. Write an expression for the total number of hours kara sings and plays the piano each week.
Answers
Answer:
(10.5 - 0.75y) hours
Step-by-step explanation:
Number of days in 1 week = 7 .
Number of days in a week Karla sings = y
Number of days Karla plays piano in a week = Number of days in 1 week - Number of days in a week Karla sings
Number of days Karla plays piano in a week = 7 - y
In 1 day Karla sings for = 45 minutes
60 minutes = 1hour
45 minutes = 1/60 * 45 = 3/4 hours = 0.75 hours
In y days time for which Karla sings = y *0.75 hours= 0.75y hours
Time for which Karla plays piano in 1 day = 1.5 hours
Time for which Karla plays piano in (7-y) day = 1.5*(7-y) hours
Total time in hours for which karla sings and plays the piano each week
= 0.75y + 1.5*(7-y)
= 0.75 y + 10.5 - 1.5y
= 10.5 - 0.75y
Thus, total number of hours karla sings and plays the piano each week is 10.5 - 0.75y hours
sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2
Answers
Answer:
D
Step-by-step explanation:
sin ( 3pi / 4 )
= sin ( pi - pi / 4 )
= sin ( pi / 4 )
= 1/root(2)
= root(2) / 2
Graph the line with slope 1/3 and y-intercept −2.
Answers
The graph of the function y = 1/3x - 2 is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
Slope = 1/3y-intercept = -2So, the equation is
y = 1/3x - 2
The above function is a linear function that has been transformed as follows
Vertically stretched by a factor of 1/3Shifted down by 2 unitsNext, we plot the graph using a graphing tool by taking note of the above transformations rules
The graph of the function is added as an attachment
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How do I add mixed numbers?
Answers
3. Which of the following is an example of overdraft protection?
A. Bank pays you interest on money in your savings account
B. Bank collects additional fees when you bounce a check
OC. ATM machine provides you with cash
D. Bank charges a large fee for bouncing a check
PLEASE HELP 4 $
Answers
Answer:
D. Bank charges a large fee for bouncing a check is not an example of overdraft protection.
Step-by-step explanation:
Overdraft protection is a service offered by banks that allows you to link your checking account to another account, such as a savings account or a line of credit. If you overdraw your checking account, the bank will automatically transfer funds from the linked account to cover the shortfall, which helps you avoid overdraft fees and other penalties.
Option A is not an example of overdraft protection as it refers to earning interest on money in your savings account, which is a separate service.
Option B refers to additional fees collected by the bank when you bounce a check, which is a penalty for not having sufficient funds in your account to cover the check.
Option C refers to an ATM machine providing you with cash, which is a basic function of an ATM and is not related to overdraft protection.
Anthony's sink is shaped like a half-sphere, and it has a volume of 700m cubic inches.
It is completely full of water, and he has two different cylindrical cups he can use to
scoop it out
The blue cup has a diameter of 4 in. and a height of 8 in., and the green cup has a
diameter of 8 in. and a height of 8 in.. How many cupfuls of water will it take for him
to empty his sink using each cup?
Answers
You will need to use the small cup 9 times or the larger cup 2 times.
How many cups he needs to use of each one?
The volume of the sink is 700 in^3
The smaller cup is a cylinder with a diameter of 4 in and a height of 8 in, its volume is:
V = 3.14*(4in/2)^2*8in = 100.48 in^3
To remove all the water in the sink you will need:
N = 700 in^3/100.48 in^3 = 6.97 = 7
You will need to scoop the water 7 times.
For the larger cup, the diameter of 8 in and a height of 8 in, its volume is:
V' = 3.14*(8in/2)^2*8in = 401.92 in^3
You will need to scoop the water:
N' = 700 in^3/401.92 in^3 = 2 times.
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I need expert answers for this
Answers
The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.
How to prove Trigonometric Identities?We want to verify the trigonometric identity;
cos (α - β)/(cos α sin β) = cot β + tan α
Now, according to trigonometric identities in mathematics, we know that;
cos (α - β) = (cos α cos β) + (sin α sin β)
Thus, plugging that back into our left hand side of the main question gives;
[(cos α cos β) + (sin α sin β)]/(cos α sin β)
Rewriting this expression by separating the denominator gives;
[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)
Using quotient identities, this can be simplified to;
cot β + tan α
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A delivery driver earns a fixed amount for each delivery she makes, and
yesterday her average hourly wage was $16.50 an hour. If she worked 6 hours
yesterday and made 11 deliveries, how much does she earn for each delivery
made?
O A. $9.90
O B. $9.00
O C. $5.50
O D. $5.00
Answers
Answer:
9 dollars or B
Step-by-step explanation:
16.50 (hourly wage) x 6 (hours worked) = 99 dollars
$99/11 deliveries= 9 dollars per delivery.
which best describes how to solve the equations below 35x=88
Answers
Use a table of values to graph the function f(x) = (x + 2- 1. Select the correct graph
below.
Answers
you can download the app called
`jae is costructing an open box froma piece of cardboard that is 9in. wide and 12in. long.
Answers
Answer:4
Step-by-step explanation:
Two angle measures of this triangle are 60°. Which type of triangle is it?
Answers
Answer:
It's an equilateral triangle.
Step-by-step explanation:
For starters, the angle measures of any triangle all add up to 180 degrees. Because 2 sides of this triangle are 60 degrees, the two sides added up would be 120 degrees. Because 180 - 120 = 60, the unknown side is 60 degrees. Because an equilateral triangle is a triangle where all the angles or sides are equal, and all of the angle measures of the triangle are equal, it is an equilateral triangle.
△ABC∼△DEF. Solve for x.
x=________
Answers
The value of x in the given similar triangles △ABC∼△DEF is 35.
What are similar triangles?
Similar triangles are those triangles in which the ratio of there common sides is always equal to each other.
As it is mentioned that △ABC∼△DEF, therefore, the two triangles are similar. Now, since in similar triangles the ratio of the sides of the triangle is same. Therefore, we can write the ratio of the sides of the triangles as,
AB/ DE = BC/EF = AC/DF
The value of x can be written as,
AB/ DE = BC/EF
25 / x = 20 / 28
x = (25 × 28) / 20
x = 35
Hence, x = 35.
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Researchers suspect that myopia, or nearsightedness, is becoming more common over time. A study from the year 2010 showed 123 cases of myopia in 400 randomly selected people. Another study from the year 2019 showed 228 cases in 600 randomly selected people. We are going to do a hypothesis test to see if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 at the 0.05 significance level.
null and alternative hypothesis ?
a. H0:P1=P2; Ha：P1≥P2
b. H0:P1=P2; Ha：P1≠P2
c. H0:P1≠P2; Ha：P1=P2
d. H0:P1≥P2; Ha：P1≠P2
Answers
Answer:
We want to test if the if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 (alternative hypothesis) , then the system of hypothesis are:
Null hypothesis: \(p_1 = p_2\)
Alternative hypothesis: \( p_1 = p_2\)
And the best option would be:
b. H0:P1=P2; Ha：P1≠P2
Step-by-step explanation:
For this case we have the following info given:
\(X_1 = 228 \) the myopia cases in 2019
\( n_1= 600\) the sample size in 2019
\( \hat p_1= \frac{228}{600}= 0.38\) estimated proportion of myopia cases in 2019
\(X_2 = 123 \) the myopia cases in 2010
\( n_2= 400\) the sample size in 2010
\( \hat p_2= \frac{123}{400}= 0.3075\) estimated proportion of myopia cases in 2010
And we want to test if the if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 (alternative hypothesis) , then the system of hypothesis are:
Null hypothesis: \(p_1 = p_2\)
Alternative hypothesis: \( p_1 = p_2\)
And the best option would be:
b. H0:P1=P2; Ha：P1≠P2
And we can conduct a two sample z proportion test in order to verify the hypothesis.
Answer:
< 0.5 \leqslant pvalue < 0.10\)answer C on khan academysolve for x. log49^x=1/2
Answers
Answer:
x = 0.295
Step-by-step explanation:
1/5/2023
7:24PM
Is 5x-8+7y=y-6 linear or nonlinear
Answers
Answer:
Step-by-step explanation:
The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.
A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/25 for black, 1/5 for yellow,1/15 for blue, and 1/10 for white. What is the probability of pulling a black or yellow card, written as a reduced fraction?
Answers
Step-by-step explanation:
P(black or yellow) = P(black) + P(yellow) − P(black and yellow)
P(black or yellow) = 1/25 + 1/5 − 0
P(black or yellow) = 6/25
39) 18% of 18 is what?
Answers
Answer:
3.24
Step-by-step explanation:
Hope this helps :)
Which of the following points would fall on the line produced by the point-slope form equation y - 10 = 3(x - 11) when graphed?
Answers
Answer:
(-5,-37)
(-4,-34)
(-3,-31)
(-2,-28)
(-1,-25)
(0,-22)
(1,-19)
(2,-16)
(3,-13)
(4,-10)
(5,-7)
(6,-4)
Step-by-step explanation:
y - 10 = 3(x - 11)
y - 10 = 3x - 33
y = 3x -22