Question 3

(a) The following graph uses the window 1 x 11, 10 y 170.

Graph of S(t) = 0.4 / (0.0025 + 160e-2.7t)

From the graph, we can estimate S(5) 147, and S'(5) 32.* This tells us that in 1995 (t = 5), sales of Humatrope had reached $147 million, and were increasing at a rate of $32 million per year.

(b) S'(10) 0, since the tangent to the graph is almost horizontal at the point where t = 10.

(c) Sales were increasing most rapidly at approximately t = 4 (1993), since the graph is steepest around that value of t.

* See Example 3 on p. 183 of Calculus Applied to the Real World for a discussion on estimating the derivative graphically.