The fungus Fusarium exosporium infects a field of flax plants through the roots and

Chapter 2, Problem 27

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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 16. (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]: Days 0 10 20 30 40 50 60 Percent infected 0 18 56 82 91 96 98 (d) Draw the tangent line at t = 40 and estimate its slope. Percent infected Days after planting 10 20 30 40 50 60 100 80 60 40 20