Answer
(a) $\frac{dy}{dt} = ky$
(b) $\frac{dP}{dt} = kP$
This is an appropriate model for population growth when the relative growth rate of the population is constant.
(c) $y(t) = y(0)e^{kt}$
Work Step by Step
(a) $\frac{dy}{dt} = ky$
The rate of change of $y$ is proportional to $y$. The constant $k$ is the relative growth rate.
(b) $\frac{dP}{dt} = kP$
This is an appropriate model for population growth when the relative growth rate of the population is constant.
(c) The solution of the differential equation in part (a) is: $y(t) = y(0)e^{kt}$
