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?

   Hint (a):

   0.40

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

   Hint (b):

   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.

   Answer (c):

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

4. When does the video have no value?

   Hint (d):

   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.