a. $26747$, point $(10,26747)$ b. underestimates by 1253. c. rises to the right, useful to some extent.
Work Step by Step
a. For $x=10$, with the given function, we have $f(10)=0.76(10)^3-30(10)^2-882(10)+37807=26747$ This means that the value from the model equation is 26747 for year $1970+10=1980$. The point is at $(10,26747)$ on the right graph. b. From the bar graph, we have $28000$ for year 1980. Thus the above value underestimates the actual data by 1253. c. The leading term is $0.76x^3$, with a coefficient of $+0.76$ and 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 models the population from year $1970$ to $2010$ fairly accurately with the population decreasing initially and rising after $x=35$ or year $2005$ as a result of the conservation efforts. Thus, it is useful to some extent.