The population of salmon next year is given by f ( S ) = S e r ( 1 - S / P) , where S is this year's salmon population, P is the equilibrium population, and r is a constant that depends upon how fast...

The population of salmon next year is given by

f ( S ) = S
e
^{r ( 1 - S / P)},

where S is this year's salmon population, P is the equilibrium 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 = 750.