Question

The accompanying bar graph shows the percentage of adults in a certain city who smoked cigarettes for selected years from 1970 through 2010.
The mathematical model p + x/2 = 33 describes the percentage, p, of adults who smoked cigarettes x years after 1970. Use this information to answer questions (a) and (b) below.

Does the mathematical model underestimate or overestimate the percentage of adults who smoked cigarettes in 2010? By how much? Select the correct choice below and fill in the corresponding answer box to complete your choice.

Answer 1

Using function concepts, we have that:

The actual percentage of smokers in 2010 was of 23%, while the estimated was of 13%, thus, the model underestimated the percentage by 10%.

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The function is:

$p + \frac{x}{2} = 33$

In which

• p is the percentage of smokers.
• x is the number of years after 1970.

The percentage can be written as a function of the number of years, that is:

$p(x) = 33 - \frac{x}{2}$

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2010 is 2010 - 1970 = 40 years after 1970, thus, the estimate of the percentage in 2010 is:

$p(40) = 33 - \frac{40}{2} = 33 - 20 = 13$

The actual percentage of smokers in 2010 was of 23%, while the estimated was of 13%, thus, the model underestimated the percentage by 10%.

A similar problem is given at brainly.com/question/24481455