Chapter 1.7, Problem 71E

(a)

To determine

To write: $g$ in terms of $f$ .

Answer to Problem 71E

  $g\left(t\right)=\frac{3}{4}f\left(t\right)$ .

Explanation of Solution

Given information:

Given graph

  

The profits were only three-fourths as large as expected

  

Calculation:

Let us consider the following graph,

  

From the description and the graph of $g\left(t\right),$ we have $g\left(t\right),$ is obtained by shrinking $f\left(t\right)$ vertically by $\frac{3}{4}$ .

The equation of new function $g\left(t\right),$ can be obtained from $f\left(t\right)$ by the following steps.

Vertical shrink of $\frac{3}{4}$ . $g\left(t\right)=\frac{3}{4}f\left(t\right)$

Hence $g\left(t\right)=\frac{3}{4}f\left(t\right)$ .

(b)

To determine

To write: $g$ in terms of $f$ .

Answer to Problem 71E

  $g\left(t\right)=f\left(t\right)+10000$

Explanation of Solution

Given information:

The profits were consistently$10000 greater than predicted.

  

Calculation:

Let us consider the following graph,

  

From the description and the graph of $g\left(t\right),$ we have $g\left(t\right),$ is obtained by shrinking $f\left(t\right)$ vertically upward by 10000.

The equation of new function $g\left(t\right),$ can be obtained from $f\left(t\right)$ by the following steps.

Vertical shift 10000 units upward. $g\left(t\right)=f\left(t\right)+10000$

Hence $g\left(t\right)=f\left(t\right)+10000$

(c)

To determine

To write: $g$ in terms of $f$ .

Answer to Problem 71E

  $g\left(t\right)=f\left(t-2\right)$ .

Explanation of Solution

Given information:

There was a two year delay in the introduction of the product. After sales began, profits grew as expected.

  

Calculation:

Let us consider the following graph,

  

From the description and the graph of $g\left(t\right),$ we have $g\left(t\right),$ is obtained by shrinking $f\left(t\right)$ horizontally right by 2 units.

The equation of new function $g\left(t\right),$ can be obtained from $f\left(t\right)$ by the following steps.

Vertical shift 2 units right. $g\left(t\right)=f\left(t-2\right)$

Hence $g\left(t\right)=f\left(t-2\right)$