Chapter 9.5, Problem 85E

(a)

To determine

To Find: The standard form for the function $g\left(t\right)$ .

Answer to Problem 85E

The standard form is $g\left(t\right)=-0.056t^2+1.06t+23.1$

Explanation of Solution

Given:

The function $f\left(t\right)$ is $f\left(t\right)=-0.056t^2+1.62t+16.4$ where $5\le t\le 14$ .

Calculation:

Consider the given function is,

  $f\left(t\right)=-0.056t^2+1.62t+16.4$

Then, the function $g\left(t\right)$ is,

  $\begin{array}{c}g\left(t\right)=f\left(t+5\right)\\ =-0.056{\left(t+5\right)}^2+1.62\left(t+5\right)+16.4\\ =-0.056\left(t^2+10t+25\right)+16.2\left(t+5\right)+16.4\\ =-0.056t^2+1.06t+23.1\end{array}$

(b)

To determine

To Find: The graph for $f$ and $g$ in the same viewing window.

Answer to Problem 85E

The required graph is shown in Figure 1

Explanation of Solution

Consider the standard form is $g\left(t\right)=-0.056t^2+1.06t+23.1$ .

The graph for the function $g\left(t\right)$ and $f\left(t\right)$ is shown in Figure 1

  

Figure 1

(c)

To determine

To Find: The graph to estimate when the child support collections exceeded $\$27$ billion.

Answer to Problem 85E

The graph is shown in Figure 2 and graph shows that the intersection is at $t=10$ that is the child support collection exceed at $\$27$ billion in 2010.

Explanation of Solution

Graph the line for $y=27$ that corresponds to $27 billion and then find the intersection wit $f\left(t\right)$ . The graph for it is shown in Figure 2

  

Figure 2

The graph shows that the intersection is at $t=10$ that is the child support collection exceed at $\$27$ billion in 2010.