Answer
$47.3$ new cases per day.
In the period from March 17 to March 23, SARS cases were growing at an average rate of $47.3$ new cases per day.
Work Step by Step
The average rate of change of $f$ over the interval $[a, b]$ is
Average rate of change of $f\displaystyle \ \ =\frac{f(b)-f(a)}{b-a}$
The units of the average rate of change of $f$ are units of $f(x)$ per unit of $x$.
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On March 17, $t=0$
On March 23, $t=6$
Average rate of change = $\displaystyle \frac{A(6)-A(0)}{6-0}=\frac{450.8255-167}{6}\approx 47.3$ new cases per day.
In the period from March 17 to March 23, SARS cases were growing at an average rate of $47.3$ new cases per day.