Chapter 1.8, Problem 60E

(a)

To determine

Find the function $p(t)$ that represents the total number of dogs and cats in the United States

Answer to Problem 60E

The function $p(t)$ that represents the total number of dogs and cats in the United States

  $p\left(t\right)=d\left(t\right)+c\left(t\right)$

Explanation of Solution

Given:

Interpret $p\left(16\right)$ and interpret $h(t)=\frac{p(t)}{n(t)}$

The number of dogs in the United States in t years is $d\left(t\right)$ and the number of cats in the United States in t years is $c\left(t\right)$ where t is the year with t=10 corresponding to 2010.

The total number of dogs and cats p(t) in the United States is

  $p\left(t\right)=\left[thenumberofdogs\right]+\left[thenumberofcats\right]$

  $p\left(t\right)=d\left(t\right)+c\left(t\right)$

Thus, $p\left(t\right)=d\left(t\right)+c\left(t\right)$

(b)

To determine

Interpret the $p(16)$

Answer to Problem 60E

The function $p(t)$ that represents the total number of dogs and cats in the United States

  $p\left(t\right)=d\left(t\right)+c\left(t\right)$

Explanation of Solution

Given:

The number of dogs in the United States in t years is $d\left(t\right)$ and the number of cats in the United States in t years is $c\left(t\right)$ where t is the year with t=10 corresponding to 2010

p(16) represents the total number of dogs and cats of the United States in the year 2016.

(c)

To determine

Find and interpret $h(t)=\frac{p(t)}{n(t)}$

Answer to Problem 60E

  $h(t)=\frac{p(t)}{n(t)}$ is interpreted below.

Explanation of Solution

Given:

The number of dogs in the United States in t years is $d\left(t\right)$ and the number of cats in the United States in t years is $c\left(t\right)$ where t is the year with t=10 corresponding to 2010

When the total numbers of dogs and cats is divided by the population of the United States in year t, then get the rate of dogs and cats in the population. So, $h(t)=\frac{p(t)}{n(t)}$