(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.