During the first year 5000 units were sold the saturation

Question

1. The cumulative sales 5 (in thousands of units) of a new product after it has been on the market for t years are modeled by

S = Ce^k/t.

During the first year, 5000 units were sold. The saturation point for the market is 30,000 units. That is, the limit of S as t → ∞ is 30,000.

a. Solve for C and k in the model.

b. How many units will be sold after 5 years?

2. A small business assumes that the demand function for one of its new products can be modeled by p = Ce^kx. When p = $45, x = 1000 units, and when p = $40, x = 1200 units. Solve for C and k.