Chapter 5.3, Problem 83E

Advertising. A company is trying to expose a new product to as many people as possible through TV ads. Suppose that the rate of exposure to new people is proportional to the num­ber of those who have not seen the product out of L possible viewers (limited growth). No one is aware of the product at the start of the campaign, and after 10 days, 33% of L are aware of the product. Mathematically,

     $\frac{dN}{dt}=k(L-N)N(0)=0N(10)=0.33L$

(A)    Solve the differential equation.

(B)    How many days will it take to expose 66% of L?

(C)    Graph the solution found in part (A) for 0 ≤ t ≤ 90.