Chapter 6.3, Problem 46E

(a)

To determine

The graph of the function with domain and range.

Answer to Problem 46E

The range is $y\ge 15$

Explanation of Solution

Given information:

The function represent of population equation as shown below,

  $y=15{\left(3\right)}^x$

Formula used:

The x axis represents the horizontal axis and the y axis represents the vertical axis.

Calculation:

Identify some points then plot & connect with a smooth line:

  

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

Conclusion:

The range is $y\ge 15$

(b)

To determine

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:

The function represent of population equation as shown below,

  $y=15{\left(3\right)}^x$

Formula used:

The x axis represents the horizontal axis and the y axis represents the vertical axis.

Calculation:

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

Conclusion:

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

(c)

To determine

The number of coyotes after 40 years.

Answer to Problem 46E

There will be 135 coyotes after 40 years

Explanation of Solution

Given information:

The function represent of population equation as shown below,

  $y=15{\left(3\right)}^x$

Formula used:

The x axis represents the horizontal axis and the y axis represents the vertical axis.

Calculation:

At x = 2 (40 years is equivalent to two 20 years)

  $\begin{array}{l}y=15{\left(3\right)}^2\\ =15\left(9\right)\\ y=135\end{array}$

There will be 135 coyotes after 40 years

Conclusion:

There will be 135 coyotes after 40 years