Chapter 5.4, Problem 5E

A Skydiver If a skydiver jumps from an airplane, his velocity $v$, in feet per second, starts at $0$ and increases towards terminal velocity, an average-sized man has a terminal $T$ of about $176$ feet per second. The difference $D=T-v$ is an exponential function of time,

a. What is the initial value of $D$?

b. Two second into fall, the velocity is $54.75$ feet per seconds. Find an exponential formula for $D$.

c. Find a formula for $v$.

d. Express the velocity $4$ seconds into the fall using functional notation, and then calculate that value.