1. ## Exponential word problems

The sales S (in thousands of units) of a new product after it has been on the market t years is

$S=Ce^{k/t}$

a. Find s as a function of t if 5,000 units have been sold after 1 year and the saturation point for the market is 30,000 (that is, lim (as t approaches infinity) S=30).

b. How many units will have been sold after 5 years?

c. Use a graphing utility to graph this sales function.

2. So the first thing is you need to find C and k. To find C, use the saturation point info they gave. As x approaches infinity, what happens to the e^{k/t} term? It goes toward e^0, or 1, which leaves you with only C. So that should tell you what C is. To find k, plug in the info they gave about 5k units sold after one year.