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picture: The population of salmon next year is given by f(S) = Ser(1-s/P), where

ID: 3344419 • Letter: P

Question

picture:

The population of salmon next year is given by f(S) = Ser(1-s/P), where S is this year's salmon population. P is the equation population, and r is a constant that depends upon how fast the population grows. Find f '(S0) and solve the equation f '(S0) = 1. using a calculator to find the intersection of the graphs f '(S0) and y = 1. Find the population for which the maximum sustainable harvest occurs if r=0.4 and P = 850. The maximum sustainable harvest occurs for a population of (Round to the nearest thousandth as needed.)

Explanation / Answer

The derivative of f(S) = e^(r(1-S/P)) - rs/pe^(r(1-s/P)

For r = .4 and P=850, we need to find where this equals 1.

I got near the solution and used the bisection method for a quick search.

The solution is approximately 403.064247669105, which rounds to 403.064