3 Suppose the population of a town is shrinking according to

3. Suppose the population of a town is shrinking according to a logistic model with initial population 1000 and carrying capacity 10,000. If the population shrinks to 682 after two years, what will the population be after 5 years? (8 pts)

Solution

M = 10000, P0 = 1000 and so A = 9,[ A = (M - P0) / P0 ]
using the formula for A. P(t) = M / ( 1 + A*e^kt ) ....
We can use the information......P(2) = 682 to find k...

682 = 10000 / ( 1 + 9*e^2k).....
solving, k = 0.2087245......

P(5) = 10000 / ( 1 + 9*e^(5*0.2087245) )

= 376.5716303 or nearly equals to 377....