### Home > PC3 > Chapter 13 > Lesson 13.2.2 > Problem13-74

13-74.

The 2017 profits, $p$, in thousands of dollars, for Functions of America is modeled by $p\left(x\right) = −x^{4} + 21x^{3} − 138x^{2} + 280x$, where $x$ is months since January 1st, 2017.

1. Approximate Functions of America’s profits for the first four months of 2017.

Approximate the area under the curve over the interval $0\le x\le4$.

2. Approximate Functions of America’s profits for the first seven months of 2017.

Approximate the area under the curve over the interval $0\le x\le7$.

3. What happened in May, June, and July?

This can be answered using your results from parts (a) and (b).

4. Did Functions of America gain or lose money in 2017? How much?

Approximate the area under the curve over the interval $0\le x\le12$.
To get an accurate approximation, you will need to use a significant number of rectangle.