Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: P(t) = d 1 + ke−ct where c, d, and k are positive constants. For a certain fish population in a small pond d = 1200, k = 11, c = 0.2, and t is measured in years. The fish were introduced into the pond at time t = 0. (a) How many fish were originally put in the pond? 100 Correct: Your answer is correct. fish (b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.) 10 years 1 Changed: Your submitted answer was incorrect. Your current answer has not been submitted. fish 20 years fish 30 years fish (c) Evaluate P(t) for large values of t. What value does the population approach as t → [infinity]? P(t) =

Answers

Answer 1

Answer:

(a) 100 fishes

(b) t = 10: 483 fishes

    t = 20: 999 fishes

    t = 30: 1168 fishes

(c)

[tex]P(\infty) = 1200[/tex]

Step-by-step explanation:

Given

[tex]P(t) =\frac{d}{1+ke^-{ct}}[/tex]

[tex]d = 1200\\k = 11\\c=0.2[/tex]

Solving (a): Fishes at t = 0

This gives:

[tex]P(0) =\frac{1200}{1+11*e^-{0.2*0}}[/tex]

[tex]P(0) =\frac{1200}{1+11*e^-{0}}[/tex]

[tex]P(0) =\frac{1200}{1+11*1}[/tex]

[tex]P(0) =\frac{1200}{1+11}[/tex]

[tex]P(0) =\frac{1200}{12}[/tex]

[tex]P(0) = 100[/tex]

Solving (a): Fishes at t = 10, 20, 30

[tex]t = 10[/tex]

[tex]P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483[/tex]

[tex]t = 20[/tex]

[tex]P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999[/tex]

[tex]t = 30[/tex]

[tex]P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168[/tex]

Solving (c): [tex]\lim_{t \to \infty} P(t)[/tex]

In (b) above.

Notice that as t increases from 10 to 20 to 30, the values of [tex]e^{-ct}[/tex] decreases

This implies that:

[tex]{t \to \infty} = {e^{-ct} \to 0}[/tex]

So:

The value of P(t) for large values is:

[tex]P(\infty) = \frac{1200}{1 + 11 * 0}[/tex]

[tex]P(\infty) = \frac{1200}{1 + 0}[/tex]

[tex]P(\infty) = \frac{1200}{1}[/tex]

[tex]P(\infty) = 1200[/tex]


Related Questions

Which graph has a y-intercept of 2 and a slope of - 1/3?

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it is the fourth graph the numbers are 24

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Answer:

If it a khan you can go take a hint and try to find it

Which type of graph would you choose to show the number of home runs hit by each player compared to the team
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histogram
line graph
bar graph
circle graph

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Answer:

circle graph

Step-by-step explanation:

Answer:

BAR GRAPH

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Convert 451 degrees Fahrenheit to Celsius

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232.778

Step-by-step explanation:

Answer:

232.778 °C

Never forget your symbols.

a)How many vertices does it have?
(b) How many edges (lateral edges plus base edges) does it have?
(c)How many faces (lateral faces plus bases) does it have?

Answers

5 vertices

7 edges

5 faces

pls I need assistance with this I promise brainiest

1. (-4)*(-3)*(+2)/(-6)*(-4)
2. -8*(-11)*9*(-5)/2*(-33)*(-3)​

Answers

Answer:

1) 16

2) -196020

Step-by-step explanation:

simple answer using DMAS rule

D = Division

M = Multiplication

A = Addition

S = Subtraction

Find the general term of series 1/2-1+2-4+

Answers

For the given sequence the general term could be defined as n/(n + 1), where 'n' is clearly a natural number.

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Answers

40 cubic units, just count them my guy

you got a chunk of 32 and a chunk that's 8

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Answers

Answer:

1 4/5 pounds each

Step-by-step explanation:

9/5 = 1 4/5

Milo visited an amusement park for 3 hours. He rodes rides for 50 minutes, played carnival games for 40 minutes, and ate food for 30 minutes. He spent the rest of the time waiting in lines. How much times did Milo spend waiting in lines?

Answers

Answer:

60 minutes

Step-by-step explanation:

3 hours = 180 minutes

180 - (50 + 40 + 30) = 180 - 120 = 60

THIS IS DUE IN AN HOUR PLS HELP !

Answers

Answer:

27

Step-by-step explanation:

Answer:

22°

Step-by-step explanation:

<1 is a secant-secant angle (it lies outside the circle, created by two lines that cut through the circle). The measure of a secant-secant angle is half the difference of the measures of the intercepted arcs:

<1=(0.5)(98-54)

<1=(0.5)(44)

<1=22°

How much is 2/9th of 234.900?

Answers

Given:

The number is 234.900.

To find:

The [tex]\dfrac{2}{9}[/tex]th of 234.900.

Solution:

We need to find the [tex]\dfrac{2}{9}[/tex]th of 234.900. So, multiply [tex]\dfrac{2}{9}[/tex] and 234.900 to get the required value.

[tex]\text{Required value}=\dfrac{2}{9}\times 234.900[/tex]

[tex]\text{Required value}=\dfrac{469.800}{9}[/tex]

[tex]\text{Required value}=52.200[/tex]

Therefore, the [tex]\dfrac{2}{9}[/tex]th of 234.900 is 52.200 or it can be written as 52.2.

Middletown High School has student elections every year. Lately, the school has seen a 5% decrease in voting from election to election. If 910 students voted this year, how many will be expected to vote 8 years from now? (Round to the nearest whole number if necessary).​

Answers

Answer:

603.71

Step-by-step explanation:

Use a function to solve this.

F(x)

Now lets put in the data for the function.

We have 910, which is the orginal number. This should be the first number, and will have to be multiplyied by the other numbers in the function to find the answer. I think of all these numbers like the things in a penut butter and jelly sandwhich, is sounds very nice since I am hungry.

F(x) = 910 *

Next, we have 5%, which is what we are taking from 910. So, we can think of this as 910 being multiplyied by 0.95. Lets add this to our growing penut butter and jelly sandwhich. The reason I put this into a parenthese is so that the 910

F(x) = 910 * (0.95)

Now for the last step, we must add in the years. So, eahc year we reduce the 910 by 5%, and we need to do this 8 years This means that the 910 times 0.95 must repeat 8 times. To do this, we need ot use exponent. This exponent is 8. So, here is our completed function:

F(x) = 910 * (0.95^8)

Lets plug this into a calculator, since doing this out on paper would be a real pain and will take far to long. I would probably die of hunger and never get a penut butter and jelly sandwhich if I did this out on paper.

In the end, you should get 603.7125 blah blah blah it goes on for a long time. I attached a file of what it looks like in the calculator if you want some evidence.

Oh, you said you want it rounded to the nearest whole number. Well, lets remember our rounding here. Anything below 5 goes down, anything 5 and higher goes up. Since we have 603.7125, we can round that too 603.71

Answer:

603.71

Ti⊂k∫∈s ω∅∅p

Im gonna go grab my PBJ now.

Solve for [?]. Assume that lines which appear tangent are tangent.

Answers

Answer:

Step-by-step explanation:

Since the problem stated that the 2 lines are tangent, you can then tell that the triangle is a right triangle.

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A man is in a lighthouse tower that is 65 ft. He spots a ship at sea at an angle of depression of 20°. How far is the ship from the base of the lighthouse to the nearest foot?

Answers

65*tan(20)=23.658 or 24

Answer:

24 feet

Step-by-step explanation:

distance away is x

tan(20)=x/65

65*tan(20)=x

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round to the nearest foot

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Answers

Answer:

i think 1 half sorry if i am wrong

Step-by-step explanation:

12
B
4
E
D
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A

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(B) 5
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Answers

Answer:

i would say B

Step-by-step explanation:

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Answers

The bottom left should be correct

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A
B
A.
3x-2x +0.5x
1.
1.5x
B.
3(x + 4)-2(x + 4)
2. x + 3
C.
6(x+4)-2(x + 5)
3. 2(2x + 7)
D.
3(x + 4)-2(x + 4) + 0.5(x + 4)
4. 1.5
For each situation write an eynression for the new balance using as few terms as possible

Answers

A. [tex]3x-2x+0.5x=1.5x[/tex], so the expressions are equivalent.

B. [tex]3(x+4)-2(x+4)=x+4[/tex], so the expressions are not equivalent. To make the expressions equivalent, add 1 to expression B.

C. [tex]6(x+4)-2(x+5)=6x+24-2x-10=4x+14=2(2x+7)[/tex], so the expressions are equivalent.

D. [tex]3(x+4)-2(x+4)+0.5(x+4)=1.5(x+4)[/tex], so the expressions are not equivalent. To make the expressions equivalent, multiply expression B by (x+4).

Four points are graphed on the number line below.



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A point w
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Answers

Answer:

It's close between Y and Z, but I'd go with Z

Step-by-step explanation:

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Answers

Answer:

A

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Answers

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Answers

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its c

Step-by-step explanation:

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Answers

2x = -5

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................

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Answers

Answer:

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Step-by-step explanation:

That's the answer I got im pretty sure it correct

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(Marking brainliest if correct)

8/17
15/17
15/8
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Answers

Answer:

15/8

Step-by-step explanation:

Assuming you mean tan theta

Tan(theta) = opposite/adjacent

We know the adjacent side is 8 so the bottom of the fraction must also be 8

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The value of tangent of the angle θ, i.e., tan θ = 15/8.

Hence the correct option is c.

Given is a right triangle, with base = 8 units and the hypotenuse is 17 units,

The angle θ which is between the base and the hypotenuse,

We need to find the value of tangent of the angle θ, i.e., tan θ.

To find the value of tangent (tan) of the angle θ, we can use the definition of tangent in a right triangle.

The tangent of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, the base of the triangle is given as 8 units, and the hypotenuse is given as 17 units.

To find the length of the side opposite θ, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we can calculate the length of the side opposite θ:

(side opposite θ)² + (base)² = (hypotenuse)²

(side opposite θ)² + 8² = 17²

(side opposite θ)² + 64 = 289

(side opposite θ)² = 289 - 64

(side opposite θ)² = 225

side opposite θ = √225

side opposite θ = 15 units

Now that we have the lengths of the side opposite θ and the side adjacent to θ, we can calculate the tangent of the angle θ:

tan θ = (side opposite θ) / (base)

tan θ = 15 / 8

Therefore, the value of tangent (tan) of the angle θ is 15/8.

Learn more about trigonometric function click;

brainly.com/question/25618616

#SPJ4

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D. 1,400 g

Answers

Answer:

D

Step-by-step explanation:

Answer:

it is D im 99% sure

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dddddddd

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111*

Step-by-step explanation:

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e. 55 miles hope that helped

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3
24
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The answer to your question you see if two equals G0 in at four equals G2
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