Chapter 1.8, Problem 59E

(a)

To determine

Find the function that represents the percent change in the population of the United States

Answer to Problem 59E

The function that represents the percent change in the population of the United States

  $c(t)=\frac{b(t)-d(t)}{p(t)}\cdot 100\text{\%}$

Explanation of Solution

Given:

The function c(t) that represent the percent change in the population of the United States and interpret c(16).

The number of births in the United States in t years is b(t) and the number of deaths in the United States in t years is d(t) where t is the year with t=10 corresponding to 2010.

The percent change c(t) in the population of the United States is

  $c(t)=\frac{[\text{the birth rate}]-[\text{the death rate}]}{[\text{the population}]}\cdot 100\text{\%}$

  $c(t)=\frac{b(t)-d(t)}{p(t)}\cdot 100\text{\%}$

Thus, $c(t)=\frac{b(t)-d(t)}{p(t)}\cdot 100\text{\%}$

(b)

To determine

Interpret the $c\left(16\right)$

Answer to Problem 59E

The function that represents the percent change in the population of the United States

  $c(t)=\frac{b(t)-d(t)}{p(t)}\cdot 100\text{\%}$

Explanation of Solution

Given:

The function c(t) that represent the percent change in the population of the United States and interpret $c\left(16\right)$

The number of births in the United States in t years is b(t) and the number of deaths in the United States in t years is d(t) where t is the year with t=10 corresponding to 2010.

  $c\left(16\right)$ represents the percent change in the population of the United States in the year 2016.