Suppose that a population grows according to a logistic model with carrying capa

Question

Suppose that a population grows according to a logistic model with carrying capacity 6400 and k = 0.0011 per year.

(c) Program a calculator or computer to use Euler's method with step size h = 1 to estimate the population after 50 years if the initial population is 1000. (Round your answer to the nearest whole number.)
P(50)=?
(d) If the initial population is 1000, write a formula for the population after t years.

Use it to find the population after 50 years and compare with your estimate in part (c). (Round your answer to one decimal place.)
P(50)=?

Explanation / Answer

(c) Given Carrying capacity K=6400

k=0.0011

step size h=1

intial population P0=1000 at time t as

then the solution to the logistic equation is p(t)=K/1+A*e-kt   where A=K- P0 / P0    then

A=6400-1000/1000

=5400/1000

=5.4

p(50)=6400/1+5.4*e^(-0.0011)*(50)

=6400/1+5.4*2.71^(-0.0011)*(50)

Note:-calculate it you will get the answer.

d) Given intial population P0=1000 at time t as

then the solution to the logistic equation is p(t)=K/1+A*e-kt   where A=K- P0 / P0   

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