Chapter 1.8, Problem 57E

(a)

To determine

To find: The function $p\left(t\right)$ that represents the total number of dogs and cats in the United States.

Answer to Problem 57E

The function for total cats and dogs is $p\left(t\right)=d\left(t\right)+c\left(t\right)$ .

Explanation of Solution

Given:

The number of year is $t=10$ .

Calculation:

Consider the difference of change in population of cats and dogs of the United States is the sum of the total number of dogs $d\left(t\right)$ and the total number of cats $c\left(t\right)$ .

Then the total pollution of the cats and dogs in the United States is,

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

(b)

To determine

To find: The interpretation for $p\left(13\right)$ .

Answer to Problem 57E

The $p\left(13\right)$ is the total number of cats and dogs in the year 2013.

Explanation of Solution

Consider the function for the change in the population of the United States is,

  $p\left(13\right)=d\left(13\right)+c\left(13\right)$

Here, $p\left(13\right)$ is total the population of the cats and dogs in the year 2013.

(c)

To determine

To find: The interpretation for $p\left(13\right)$ .

Answer to Problem 57E

The expression for $h\left(t\right)$ is $h\left(t\right)=\frac{d\left(t\right)+c\left(t\right)}{n\left(t\right)}$ and it is the number of dogs and the cats per capita.

Explanation of Solution

Given:

The population of United states is $n\left(t\right)$ .

The given expression is,

  $h\left(t\right)=\frac{p\left(t\right)}{n\left(t\right)}$

Calculation:

Consider the population of the United States is,

  $\begin{array}{c}h\left(t\right)=\frac{p\left(t\right)}{n\left(t\right)}\\ =\frac{d\left(t\right)+c\left(t\right)}{n\left(t\right)}\end{array}$

Here, the function $h\left(t\right)$ is the number of dogs and the cats per capita.