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.
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:
[tex]R = \frac{f(b) - f(a)}{b - a}[/tex]
In this problem, the function which gives the number of flu patients after d days, [tex]0 \leq d \leq 21[/tex], is of:
[tex]f(t) = 10^{0.12d}[/tex]
Hence:
[tex]f(0) = 10^{0.12(0)} = 10[/tex]
[tex]f(21) = 10^{0.12(21)} = 124.3[/tex]
Then, the rate is:
[tex]R = \frac{124.3 - 10}{21 - 0} = 5.44[/tex]
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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