Answer
a. Rises to the right.
b. No
c. Falls to the right.
b. Somewhat useful.
Work Step by Step
a. The leading term of the function $f$ is $81x^3$, with a coefficient of $81$ and an odd power. Thus, we can identify its end behaviors as $x\to\infty, y\to \infty$; that is, the curve rises to the right.
b. No, the model predict an increase in the cut down rate, while the rate should decrease over time if the trend continues.
c. The leading term of the function $g$ is $-15x^4$, with a coefficient of $-15$ and an even power. Thus, we can identify its end behaviors as $x\to\infty, y\to -\infty$; that is, the curve falls to the right.
b. The model is somewhat useful. The model predicts a decrease in the cut down rate, which agrees with the fact that the rate will decrease over time if the trend continues. However, the model also eventually predicts a negative value for "forest cleared", which is not possible.
