Chapter 8.2, Problem 3QCE

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

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

(b) In terms of k, the half-life of the quantity is $\text{\_\_\_\_\_}\text{.}$

(c) If $y_0=y(0)$ is the initial amount of the quantity, then an explicit formula for $y\left(t\right)$ is given by $y\left(t\right)=\text{\_\_\_\_\_}\text{.}$