Chapter 3.5, Problem 89E

The 2003 SARS Outbreak In the early stages of the SARS (severe acute respiratory syndrome) epidemic in 2003, the number of reported cases could be approximated by

$A\left(t\right)=167{\left(1.18\right)}^t\left(0\le t\le 20\right)$

t days after March 17,2003 (the first day in which statistics were reported by the World Health Organization.)

a. What, approximately, was the instantaneous rate of change of $A\left(t\right)\text{ on March }27\left(t=10\right)$? Interpret the result.

b. Which of the following is true? For the first 20 days of the epidemic, the instantaneous rate of change of the number of cases

(A) increased. (B) decreased.

(C) increased and then decreased.

(D) decreased and then increased.