Answer
a. $82.3$ million.
b. decreasing.
c. $2020$.
Work Step by Step
Given the model equation $A=82.3e^{-0.004t}$, we have:
a. In year 2010, $t=0$, we have $A=82.3e^{0}=82.3$ million.
b. Because the growth rate is $-0.004$, a negative number, the population is decreasing.
c. Let $A=79.1$, we have $82.3e^{-0.004t}=79.1$; thus $t=-\frac{ln(79.1/82.3)}{0.004}\approx10$ corresponding to year $2010+10=2020$.
