Question

Monthly sales, in thousands, of a new laptop computer grow according to the model
N(t)=4.7te^-0.3t
where t is the number after introduction. Determine the point of diminishing returns and interpret your answer.

Answer 1

well, what does diminishing returns mean? Sales decrease while numbers increase.

So, you want to find t for max N.

Answer 2

the point at which the growth of a function begins to slow down

Answer 3

good call. So, rather than being where f' goes negative, it is where f' starts decreasing: where f" goes negative. That is, when the graph changes from concave up to concave down.

Unfortunately, this graph starts out concave down, so the growth rate is always decreasing, and then it starts increasing at t = 20/3

http://www.wolframalpha.com/input/?i=4.7te%5E(-0.3t)+,+0%3Ct%3C20

Answer 4

ty!