Question

) Find the average rate of change of F over the first three weeks, i.e. 0<_d<_ 21. Show the calculation that
leads to your answer. Give proper units and round your answer to the nearest tenth. What is the physical
interpretation of your answer?

Answer 1

The average rate of change of the function is of 5.44, which means that each day, there are 5.44 new cases on average.

What is the average rate of change?

The average rate of change of a function is given by the change in the output divided by the change in the input, that is, considering a function f(t) on an interval [a,b], the rate is:

$R = \frac{f(b) - f(a)}{b - a}$

In this problem, the function which gives the number of flu patients after d days, $0 \leq d \leq 21$, is of:

$f(t) = 10^{0.12d}$

Hence:

$f(0) = 10^{0.12(0)} = 10$

$f(21) = 10^{0.12(21)} = 124.3$

Then, the rate is:

$R = \frac{124.3 - 10}{21 - 0} = 5.44$

The average rate of change of the function is of 5.44, which means that each day, there are 5.44 new cases on average.

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