Apopulation of size p (in millions) varies in time t (in years) according to a logistic equation of the form
dp/dt = p(4 − p) if the initial population size is p(0) = 1 find the population for all time

The ODE is separable, with

Split up the left side into partial fractions:

Then integrating both sides gives

Given that , we find

so that the population is given by the model

or

10

step-by-step explanation:

soo this can be solve by using the formula:

f = p( 1 + i)^ n

where f is the future profit

p is the initial profit

i is the percent increase

n is the number of years

a . f = 30000 ( 1.05)^n

b. f = 30000 ( 1.05)^15

f = $62,368