Chapter 1.2, Problem 17E

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

Growth in Height The following table gives, for a certain man, his height $H=H\left(t\right)$ in inches at age $t$ in years.

$t=Age\left(years\right)$	$H=Height$ (inches)
$0$	$21.5$
$5$	$42.5$
$10$	$55.0$
$15$	$67.0$
$20$	$73.5$
$25$	$74.0$

a. Use functional notation to express the height of the man at age $13$, and then estimate its value.

b. Now we study the man’s growth rate.

i. Make a table showing, for each of the $5$-year periods, the average yearly growth rate-that is, the average yearly rate of change in $H$.

ii. During which $5$-year period did the man grow the most in height?

iii. Describe the general trend in the man’s growth rate.

c. What limiting value would you estimate for the height of this man? Explain your reasoning in physical terms.