### Home > A2C > Chapter 3 > Lesson 3.1.4 > Problem3-53

3-53.

Assume that a DVD loses $60\%$ of its value every year it is in a video store. Suppose the initial value of the DVD was $\80$.

1. What multiplier would you use to calculate the video’s new values?

$100% − 60%$

2. What is the value of the DVD after one year? After four years?

Use your multiplier from part (a) to calculate these values.

3. Write a continuous function, $V\left(t\right)$, to model the value of a DVD after $t$ years.

$V\left(t\right) = 80\left(0.4\right)^{t}$

4. When does the video have no value?

Let $V\left(t\right) = 0$ in the equation in part (c).
Solve for $t$. What happens?

5. Sketch a graph of this function. Be sure to scale and label the axes.

Completed the table in the eTool below for part (e) of this problem.
Click on the link at right for the full eTool version: 7-48 HW eTool