Chapter 5.1, Problem 1CYU

a. Solve the differential equation $P\text{'}\left(t\right)=-0.6P\left(t\right),P\left(0\right)=50$.

b. Solve the differential equation $P\text{'}\left(t\right)=kP\left(t\right),P\left(0\right)=4000$, where $k$ is some constant.

c. Interpret the meaning of $P\left(2\right)=100P\left(0\right)$, where $t$ is in hours.

d. Find the value of $k$ in part $(b)$ for which $P\left(2\right)=100P\left(0\right)$.