Answer
a. $f(40)= 3167$, point $(40,3167)$
b. underestimates by 33.
c. $x\to\infty, y\to\infty$, not useful.
Work Step by Step
a. For $x=40$, with the given function, we have $f(40)=0.76(40)^3-30(40)^2-882(40)+37807=3167$
This means that the value from the model equation is 3167 for year $1970+40=2010$. The point is at $(40,3167)$ on the right graph.
b. From the bar graph, we have $3200$ for year 2010; thus the above value underestimates the actual data by 33.
c. The leading term is $0.76x^3$ with a coefficient of $+0.76$ and an odd power. Thus the end behavior to the right is that $x\to\infty, y\to\infty$ -- that is, the curve will rise to the right. This function will not be useful because it predicts an infinite population of tigers as time extends, which is not possible.
