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The percentage of high school students who drink and drive was 17.5% at the beginning of 2001 and declined linearly to 10.3% at the beginning of 2011.†(a) Find a linear function f(t) giving the percentage of high school students who drink and drive in year t, where t = 0 corresponds to the beginning of 2001.f(t) = (b) If the trend continued, what was the percentage of high school students who drank and drove at the beginning of 2015? %



Answer :

Solution

Part A

For this case we have the following information given:

t= 2001 (0) f(0)= 17.5%

t= 2011 (10) f(10)= 10.3

We can calculate the slope on this way:

[tex]m=\frac{10.3-17.5}{10-0}=-0.72[/tex]

Then we can do the following:

10.3 = -0.72*10 +b

b= 10.3 +10*0.72= 17.5

Then the equation is:

f(t) = -0.72t + 17.5

Part B

For 2015 the value of t = 2015-2001= 14

Replacing we got:

f(14)= -0.72*14 + 17.5= 7.42

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