The fungus Fusarium exosporium infects a field of flax plants through the roots and causes the plants to wilt. Eventually, the entire field is infected. The percentage f (t) of infected plants as a function of time t (in days) since planting is shown in Figure 15.
(a) What are the units of the rate of change of f (t) with respect to t? What does this rate measure?
(b) Use the graph to rank (from smallest to largest) the average infection rates over the intervals [0, 12], [20, 32], and [40, 52].
(c) Use the following table to compute the average rates of infection over the intervals [30, 40], [40, 50], [30, 50].

(d) Draw the tangent line at t = 40 and estimate its slope.

Transcribed Image Text:

Days Percent infected 0 18 56 82 91 96 98 0 10 20 30 40 50 60 100 80 60 40 20 Percent infected 10 20 30 40 50 60 Days after planting FIGURE 15