Chapter 7.6, Problem 44PPS

a.

To determine

To describe: The transformation in $w\left(x\right)$ as it relates to the parent function $f\left(x\right)={\left(1.03\right)}^x$ .

Explanation of Solution

Given:

The function $w\left(x\right)=130{\left(1.03\right)}^x$ .

Calculation:

Since $w\left(x\right)=130f\left(x\right)$ , the function $w\left(x\right)$ is obtained by stretching the parent function $f\left(x\right)={\left(1.03\right)}^x$ in y -direction by a factor of 130.

b.

To determine

To find: The starting weight of the person R.

Answer to Problem 44PPS

95 pounds.

Explanation of Solution

Given:

The function $v\left(x\right)=95{\left(1.03\right)}^x$ represents the weight that the person R can lift after x weeks.

Calculation:

To find the starting weigth of the person R, substitute $x=0$ in the given function and simplify the result.

  $\begin{array}{c}v\left(0\right)=95{\left(1.03\right)}^0\\ =95\cdot 1\\ =95\end{array}$

So, the person R’s starting weight is 95 pounds.

c.

To determine

To compare: The two functions $w\left(x\right)$ and $v\left(x\right)$ .

Explanation of Solution

Given:

The functions $w\left(x\right)=130{\left(1.03\right)}^x$ and $v\left(x\right)=95{\left(1.03\right)}^x$ .

The starting point for $w\left(x\right)$ is $\left(0,130\right)$ whereas the starting point of $v\left(x\right)$ is $\left(0,95\right)$ .

The graph of the function $w\left(x\right)$ rises at higher rate as compared to the graph of the function $v\left(x\right)$ .