Chapter 11.2, Problem 24E

a.

To determine

To graph: the given functions.

Answer to Problem 24E

Explanation of Solution

Given:

The given function is:

The average national teacher salary can be molded using the equation $y=9.25{\left(1.06\right)}^n$ , where y is the salary in thousand in dollars and n is the number of years since 1970.

Calculation:

According to the question,

Create the table by using the equation $y=9.25{\left(1.06\right)}^n$ and draw the graph of the given function.

$x$	$9.25{\left(1.06\right)}^n$
$0$	$9.25$
$1$	$9.805$
$4$	$11.677912$
$6$	$13.121$
$10$	$29.6660$
$20$	$53.127$

The graph of $y=9.25{\left(1.06\right)}^n$

is given below:

Hence, thegraph of $y=-5^x$ is a reflection of $y=5^x$ across the x-axis. The graph of $y=5^{-x}$ is a reflection of $y=5^x$ across the y-axis

b.

To determine

To find: theexpect the salary of teacher in the year 2020.

Answer to Problem 24E

  $y=\$170.387\text{thousand}$ .

Explanation of Solution

Given:

The average national teacher salary can be molded using the equation $y=9.25{\left(1.06\right)}^n$ , where y is the salary in thousand in dollars and n is the number of years since 1970.

Calculation:

From the graph in part (a),

Firstdetermine the difference between 2020 and 1970:

  $2020-1970=50$

According to the question,

  $\begin{array}{l}y=9.25{\left(1.06\right)}^n\\ y=9.25{\left(1.06\right)}^{50}\{\therefore n=50\}\\ y=\$170.387\text{thousand}\end{array}$ .

Hence, the expect the salary of teacher in the year 2020 is $y=\$170.387\text{thousand}$ .