Chapter 1.3, Problem 37E

a.

To determine

To find: the zero of function and explain its meaning.

Answer to Problem 37E

  $\left(36,0\right)$

The zero represents that the lifespan of an asset is less than 36 months or 3 years.

Explanation of Solution

Given information:

The given variables are as follows:

Value of a piece of software = $v\left(t\right)$

Number of months = $t$

The equation for $v\left(t\right)$ is as follows:

  $v\left(t\right)=10440-290t$

Calculation:

Rearrange the given equation with slope intercept form as follows:

  $\begin{array}{l}y=mx+b\\ v\left(t\right)=-290t+10440\\ \therefore y=v\left(t\right),x=t\end{array}$

Put $v\left(t\right)=0$ in the given equation and solve to find the zero of function as shown below.

  $\begin{array}{c}0=10440-290t\\ 290t=10440\\ t=\frac{10440}{290}\\ =36\end{array}$

Thus, the zero of function is $\left(36,0\right)$ .

The zero of function $\left(36,0\right)$ represents that the value of an asset after 36 months is zero. Thus, the lifespan of an asset is less than 36 months.

b.

To determine

To find: the slope and explain its meaning.

Answer to Problem 37E

  $m=-290$

The slope represents as the time increases, the value of assets decreases by 290 per month.

Explanation of Solution

Given information:

The given variables are as follows:

Value of a piece of software = $v\left(t\right)$

Number of months = $t$

The equation for $v\left(t\right)$ is as follows:

  $v\left(t\right)=10440-290t$

Calculation:

Rearrange the given equation with slope intercept form as follows:

  $\begin{array}{l}v\left(t\right)=10440-290t\\ v\left(t\right)=-290t+10440\\ \text{Compare with }y=mx+b\\ \therefore m=-290\end{array}$

Thus, the slope value is $-290$ .

The slope represents that at the time of purchase, the value of the asset is 10,440. As the time increases, the value decreases by 290 per month.

c.

To determine

To graph: the function.

Answer to Problem 37E

  

Explanation of Solution

Given information:

The given variables are as follows:

Value of a piece of software = $v\left(t\right)$

Number of months = $t$

The equation for $v\left(t\right)$ is as follows:

  $v\left(t\right)=10440-290t$

Zero of function = $\left(36,0\right)$

Calculation:

The zero of function $\left(36,0\right)$ represents the x- intercept.

Rearrange the given equation with slope intercept form as follows:

  $\begin{array}{l}v\left(t\right)=10440-290t\\ v\left(t\right)=-290t+10440\\ \text{Compare with }y=mx+b\\ \therefore y=v\left(t\right)\text{ and }x=t\end{array}$

Put $t=0$ in the given equation and evaluate y- intercept as follows:

  $\begin{array}{c}v\left(t\right)=10440-290\left(0\right)\\ =10440\end{array}$

Thus, the y- intercept is $\left(0,10440\right)$ .

Now, plot the graph for point coordinates $\left(0,10440\right)$ and $\left(36,0\right)$ as shown below.