## Thinking Mathematically (6th Edition)

(a) Consider the equation as follows: $p+\frac{x}{2}=37$ Now, substitute the value of $x$as $\left( 2000-1970 \right)$and find the value of $p$. p+( 2000-1970)/{2}=37 p+{30}/{2}=37 p=37-15 =22% Here, the value of x represents the number of year after 1970. Due to this, 2000 is subtracted from 1970. This shows that the mathematical model underestimates the percentage of American adults who smoked cigarettes in 2000 as given in the graph. Now, subtract the above value of the percentage of American adults who smoked cigarettes in 2000 from the given percentage of American adults who smoked cigarettes in 2000. We obtain: $23-22=1%$ Thus, the percentage is 22% and the mathematical model underestimates by 1%. (b) Consider the equation as follows: $p+\frac{x}{2}=37$ Now, substitute the value of $p$as $2$and find the value of $x$. 2+{x}/{2}=37 {x}/{2}=37-2 x=70 Here, the value of x represents the number of year after 1970. Now, the above conclusion gives the year as, \begin{align} & y=1970+x \\ & =1970+70 \\ & =2040 \end{align} Thus, this shows that only 2% Americans will smoke cigarettes in the year 2040.