A population Pt grows at a rate that is proportional to the

A population. P(t), grows at a rate that is proportional to the amount present at time t. There is initially 100 people present Write the differential equation that models this situation. DO NOT SOLVE THE DE. Include the initial condition.

Solution

let P(t) be population after time t

change in population is proportional population at that time

=>

dP/dt = kP

where k is constant

and P(0) = 100

hence differential equation is

P’ - kP =0 , P(0) = 100 where P’ = dP/dt