Chapter 5.1, Problem 55E

An Initial Value Problem Suppose that the function $P\left(t\right)$ satisfies the differential equation

$y\text{'}\left(t\right)=-.5y\left(t\right),y\left(0\right)=10$.

a. Find an equation of the tangent line to the graph of $y=P\left(t\right)$ at $t=0$. [Hint: What are $P\text{'}\left(0\right)$ and $P\left(0\right)$?]

b. Find $P\left(t\right)$.

c. What is the time constant of the decay curve $y=P\left(t\right)$?