Answer
(a) The model underestimates the percentage by $2$%.
(b) Year $2010$
Work Step by Step
(a) To answer this, we need to re-arrange the mathematical model to find $p$:
$$p = 37 - \frac{x}{2}$$
$x$ is the amount of years after 1970, so for 2010, we need to subtract both dates: $2010 - 1970 = 40$. Now, we solve for $p$:
$$p = 37 - \frac{(40)}{2} = 37 - 20 = 17$$
By looking at the graph, we see that the percentage reported is 19%, meaning that the mathematical model $underestimates$ the percentage by $19 - 17 = 2$%.
(b) To answer this, we need to re-arrange the mathematical model to find $x$: $$x = (37 - p)\times 2$$ Using the given percentage ($17$%), we can solve for $x$: $$x = (37 - [17]) \times 2 = (20) \times 2 = 40$$ Since $x$ is the amount of years after 1970, we only need to add the two to reach the year $1970 + 40 = 2010$.
