Chapter 6.1, Problem 46E

a.

To determine

To graph: the function and describe the domain and range.

Answer to Problem 46E

The time must be nonnegative so the domain is $x\ge 0.$ It follows that the range is $y\ge 15$ .

Explanation of Solution

Given information: The function $y=15{(3)}^x$ represents the population of coyotes in

national park triples, where x is the number of 20 −year period.

Calculation:

Identify some points then plot and connect with a smooth line.

Graph $y=15{(3)}^x$ is shown below.

  

The time must be nonnegative so the domain is $x\ge 0.$ It follows that the range is $y\ge 15$ .

b.

To determine

To find: and interpret the y -intercept.

Answer to Problem 46E

The y -intercept is (0, 15) $\to$ b = 15 which is represents the initial population of the coyotes.

Explanation of Solution

Given information:

Calculation:

The y -intercept is (0, 15) $\to$ b = 15 which is represents the initial population of the coyotes.

c.

To determine

To find: how many coyotes are in the national park in 40 years.

Answer to Problem 46E

There will be 135 coyotes after 40 years.

Explanation of Solution

Given information: $y=15{(3)}^x$

Calculation:

  $\begin{array}{}$ y=15{(3)}^x$$ x=2$$ y=15{(3)}^2=15\times 9=135$\end{array}$

Therefore, there will be 135 coyotes after 40 years.