Underage smoking. the number of underage cigarette smokers (ages 10–17) has declined in the united states. the peak percent was in 1998 at 49%. in 2006 this had dropped to 36%. let t be time in years after 1998 (t = 0 corresponds to 1998). a. find a quadratic function that models the percent of underage smokers as a function of time. let (0, 49) be the vertex. b. now that you have the model, predict the percent of underage smokers in 2010.

Let f(t) be the percentage of underage cigarette smokers t years after 1998.

We are also given that percentage of underage cigarette smokers was 49% (highest) in year 1998.

(A) We are supposed to assume (0,49) as vertex of our model.

Let us assume that our quadratic model is:

Upon substituting the vertex (h,k) = (0,49), we get:

We can find the value of 'a' using the fact that in year 2006 (t = 8) there were 36% underage smokers.

Therefore, the required quadratic model is

(B) In order to predict the percentage of underage smokers in year 2010, we will substitute t=12 in our quadratic model.

Therefore, there were 19.75% underage smokers in year 2010.