Answer
a. $6.8$ million.
b. $18.4$ million, underestimates by 0.4 million.
c. $25.1$ million.
Work Step by Step
a. In 1970, we have $t=0$ and $f(0)=\frac{25.1}{1+2.7e^{0}}=\frac{25.1}{3.7}\approx6.8$ million.
b. In 2010, we have $t=2010-1970=40$ and $f(40)=\frac{25.1}{1+2.7e^{-0.05(40)}}\approx18.4$ million. Compare to 18.8 million, the model underestimates the value by 0.4 million.
c. When $t\to\infty$, we have $f\to 25.1$ million which gives the limiting size of the population.
