Answer
(a) Underestimates the percentage by 1%.
(b) Year 2040.
Work Step by Step
(a) To answer this question, we must first re-arrange the mathematical model to solve for $p$: $$p + \frac{x}{2} = 37$$$$p = 37 - \frac{x}{2}$$ Since the exercise describes $x$ as the years after 1970, for the year 2000: $x = 2000 - 1970 = 30$. Therefore, $$p = 37 - \frac{(30)}{2} = 37 - 15 = 22$$ which underestimates the percentage reported by the CDC, which was 23%, by 1%.
(b) To project the year, we must once again re-arrange the mathematical model this time to solve for $x$: $$x = 2\times(37 - p)$$ By using 2% as $p$, we get the following: $$x = 2\times(37 - [2]) = 2\times35 = 70$$ Since $x$ represents the number of years after 1970, we can conclude that the year when only 2% of American adults will smoke cigarettes will be 1970 + 70 = $2040$
