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the percentage of people age 18-24 who smoke has dropped from 5.2% in 2001 to 3.4% in 2004. Calculate the percentage of people age 18-24 who smoked in 2003 and estimate the percentage of people age18-24 who smoked in 2008
 Feb 28, 2014
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grammy:

the percentage of people age 18-24 who smoke has dropped from 5.2% in 2001 to 3.4% in 2004. Calculate the percentage of people age 18-24 who smoked in 2003 and estimate the percentage of people age18-24 who smoked in 2008



the only (main) really confusing part of this question, for you i mean, is that the percentages quoted have got nought to do with the percent reduction of smokers. if you change the percentages given to decimals that may help a little.

S = P(1-r) n
P is the initial percentage = 5.2% = 0.052
S is the future percentage
n is the number of years since 2001
r is the yearly percent decrease in smokers percentage

0.034 = 0.052(1-r) 3

0.653846 = (1-r) 3

0.653846 1/3 = 1-r

r = 1 - 0.653846 1/3

r = 0.132

so the percentage of smokers is decresing by an aveerage of 13.2% per annum

S = 0.052 * (1-0.132) n
S = 0.052 * 0.868 n

For 2003, n=2
S = 0.052 * 0.868 2
= 0.039
that is, in 2003, 3.9% of the age group smoked.
Always check that your answer is sreasonable. This is between the 2001 and the 2004 values so sounds reasonable

You can do 2008 yourself.
 Mar 1, 2014

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