In recent years, the percentage of the U.S, population age 18 and older who smok

Question

In recent years, the percentage of the U.S, population age 18 and older who smoke has decreased at a roughly constant rate, from 23.3% in 2000 to 19.3% in 2010. a) Find the function describing the linear relationship. b) At what rate is the percentage of smoking population decreasing? c) If the decline in smoking continues at the same rate, will the percentage of U.S. adults who smoke reduce to 12% or less by the year 2020? d) According to this model, when will we see 0% of the U.S. adult population smoke? What do you think about this prediction?

Explanation / Answer

let the population be 100

the population that smoke in 2000 is 23.3

and the population that smoke in 2010 will be 19.3

slope = ( 19.3 - 23.3 ) / 10

slope = - 0.4

function becomes

y = - 0.4 x + 23.3

b) smoking population is decreasing at a rate of .4*100 = 40%

c) by the year 2020 smoking population will be

y = -0.4(20) + 23.3

y = 15.3 %

so it will be more than 12%

d) plug y = 0

0 = -0.4x + 23.3

-23.3 = -0.4x

x = -23.3 / -0.4

x = 58.25

smoking population will be 0 % by 2058 approximately

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