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drek231 [11]
3 years ago
14

Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p)

are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
6 0

Answer:

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is 202500 swordfishes.

Step-by-step explanation:

Let be f(p) = -0.01\cdot p^{2}+9\cdot p, the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)

First Derivative Test

f'(p) = -0.02\cdot p +9

Let equalize the resulting expression to zero and solve afterwards:

-0.02\cdot p + 9 = 0

p = 450

Second Derivative Test

f''(p) = -0.02

This means that result on previous part leads to an absolute maximum.

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is:

f(450) = -0.01\cdot (450)^{2}+9\cdot (450)

f(450) =2025

The maximum sustainable yield is 202500 swordfishes.

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The number of ants in his farm after 12 weeks is 218.

Step-by-step explanation:

Step 1:

It is given that there are 15 ants initially and the ant population increases by 25% each week.

This is an exponential rate of increase that can be modeled by the following equation:

Number of ants after n weeks = Initial number of ants * (1 + rate of increase) ^{n}

Step 2:

Rate of increase = 25% = 25 / 100 = 0.25

Number of weeks = 12

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Step 3:

Answer:

The number of ants in his farm after 12 weeks is 218.

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Step-by-step explanation

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