Because of restoration of an island habitat the maximum population of birds it c

Question

Because of restoration of an island habitat the maximum population of birds it can support at a time t is given by t/80 1000 E The growth rate of the population p(t) is equal to 1/20 of the difference between the maximum population and the current population. Initially the island has a population of 200 birds. This problem can be written as a differential equation of the form p' + f(t) p = g(t) What is f(t) in this case? f(t) = Enter just an expression. What is g(t) in this case? g(t) = Enter just an expression. What is the integrating factor Phi(t) in this case? Phi(t) = Enter just an expression for Phi(t). What did you calculate for the following antiderivative? g(t) Phi(t) dt = Enter just an expression. What is the solution to the initial value problem? p(t) = Enter just an expression for p(t), do not enter an equation.

Explanation / Answer

1) 1/20
2) 50E^(t/80)
3) = e^(t/20)

4)800*e^(t/16)

5)800*e^(t/80)

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