Chapter 9.9, Problem 32HP

(a)

To determine

To calculate: To analyze the graph of an exponential function by describing how change of $c$ increase in $y=a^x+c$ affects the graph of the function.

Answer to Problem 32HP

The increase in value of $c$ increases the y-intercept of the exponential graph

Explanation of Solution

Given information: Exponential equation $y=a^x+c$

Calculation:

Given the exponential equation as follows:

  $y=a^x+c$

Let $a=2$

Consider two values of $c$ , $c=10$ and $c=20$

When $c=10$

Exponential equation is as follows:

  $y=2^x+10$

When $c=20$

Exponential equation is as follows:

  $y=2^x+20$

Graph of above exponential functions are

  

Thus, as value of $c$ increases, the y-intercept of the exponential graph increases

Conclusion:

Hence, increase in value of $c$ increases the y-intercept of the exponential graph

(b)

To determine

To calculate: To analyze the graph of an exponential function by describing how change of decrease in $a$ for $a>1$ in $y=a^x+c$ affects the graph of the function

Answer to Problem 32HP

As value of $a$ decreases the graph of exponential function comes closer to y-axis

Explanation of Solution

Given information: Exponential equation $y=a^x+c$

Calculation:

Given the exponential equation as follows:

  $y=a^x+c$

Let $c=10$

Consider two values of $c$ , $a=4$ and $a=2$

When $a=4$

Exponential equation is as follows:

  $y=4^x+10$

When $a=2$

Exponential equation is as follows:

  $y=2^x+20$

Graph of above exponential functions are

  

For $a>1$ , as value of $a$ decreases, the graph comes closer to y-axis

Conclusion:

Hence, as value of $a$ decreases the graph of exponential function comes closer to y-axis