A population satisfies the differential equation with and

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A population satisfies the differential equation

\frac{dy}{dt}=ky

with

y(1)=200

and

y(3)=320

. Determine (i) the value of

k

and (ii) the ratio of the instantaneous growth rate at

t=3

to that at

t=1