Chapter 6.4, Problem 72E

(a)

To determine

f is an exponential growth function.

Answer to Problem 72E

The y and x get increases simultaneously.

Explanation of Solution

Given information:

The given graph of f and g as given below,

  

Formula used:

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

Calculation:

Because y increases as x increases

Conclusion:

The y and x get increases simultaneously.

(b)

To determine

The value of K.

Answer to Problem 72E

The value of k is 4

Explanation of Solution

Given information:

The given graph of f and g as given below,

  

Formula used:

  $f\left(t\right)$ is multiplied by 4 to obtain the graph of $g\left(t\right)$

Calculation:

Notice that the y-values of $f\left(t\right)$ is multiplied by 4 to obtain the graph of $g\left(t\right)$ . Therefore, $g\left(t\right)=4f\left(t\right)$ & thus, $k=4$

Conclusion:

The value of k is 4

(c)

To determine

The value of r.

Answer to Problem 72E

The value of r is 2

Explanation of Solution

Given information:

The given graph of f and g as given below,

  

Formula used:

one-to-one property

Calculation:

Substitute the function:

  $h\left(t\right)=2^{t+r}$

Therefore, from (b),

  $\begin{array}{l}g\left(t\right)=4{\left(2\right)}^t\\ g\left(t\right)=2^{t+r}\end{array}$

Rewrite 4 as base of 2:

  $2^2{\left(2\right)}^t=2^{t+r}$

To multiply common bases, add the exponents:

  $2^{t+2}=2^{t+r}$

By one-to-one property,

  $r=2$

Conclusion:

The value of r is 2