Chapter 4.3, Problem 13E

Reminder Round all answers to two decimal places unless otherwise indicated.

A Skydiver When a skydiver jumps from an airplane, his downward velocity increases until the force of gravity matches air resistance. The velocity at which this occurs is known as the terminal velocity. It is the upper limit on the velocity that a skydiver in free fall will attain (in a stable, spread position), and tor a man 01 average size, its value is about 176 feet per second (or 120 miles per hour). A skydiver jumped from an Airplane, and the difference $D=D\left(t\right)$ between the terminal velocity and his downward velocity in feet per second was measured at 5-second intervals and recorded in the following table.

$t=seconds$ into free fall	$D=velocitydifference$
$0$	$176.00$
$5$	$73.61$
$10$	$30.78$
$15$	$12.87$
$20$	$5.38$
$25$	$2.25$

a. Show that the data are exponential and find an exponential model for $D$. (Round all your answers to two decimal places.)

b. W hat is the percentage decay rate per second for the velocity difference of the skydiver? Explain in practical terms what this number means.

c. Let $V=V\left(t\right)$ be the skydiver's velocity t seconds into free fall. Find a formula for $V$.

d. How long would it take the skydiver to reach 99% of terminal velocity?