Answer
i) $a=12,000$
ii) $k=-12.2 \%$.
iii) $b= 0.8851$.
iv) $r=-11.49 \%$.
Work Step by Step
Given $P=12,000 e^{-0.122 t}$
i) We have $a=12,000$. This tells us that in year $t=0$ the population begins with 12,000 members.
ii) $k=-0.122=-12.2 \%$. This tells us that the population is decreasing at a continuous annual rate of $12.2 \%$.
iii) $b= e^k=e^{-0.122}=0.8851$. This is the annual growth factor; since it is less than 1 , we know the population is decreasing.
iv) Finally, $r=b-1=-0.1149=-11.49 \%$. This tells us that the population decreases by $11.49 \%$ each year.
