Chapter 8.2, Problem 2QCE

Suppose that a quantity $y=y\left(t\right)$ has an exponential growth model with growth constant $k>0.$

(a) $y\left(t\right)$ satisfies a first-order differential equation of the form $dy/dt=\text{\_\_\_\_\_}\text{.}$

(b) In terms of k, the doubling time of the quantity is $\text{\_\_\_\_\_}\text{.}$

(c) If $y_o=y\left(0\right)$ is the initial amount of the quantity, then an explicit formula for $y(t)=\text{\_\_\_\_\_}\text{.}$