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?

   Answer (a):

   $0.40$

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

   Answer (b):

   The DVD will be worth $$32$ after one year and $$2.05$ after four years.

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

   Answer (c):

   $V(t) = 80(0.4)^t$

4. When does the video have no value?

   Hint (d):

   When does $V(t) = (0)$? Is this consistent with reality?

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