Question

The percentage of high school students who drink and drive stood at 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 20

Answer 1

Based on this data the point representing percentage of students who drink and drive in 2001 will be (1, 17.5).

The point representing the data of 2011 will be (11, 10.3). 

We have two points. Using these two points we can find the equation of the line.

Slope of the line = $\frac{10.3-17.5}{11-1} =-0.72$

Using the point slope form of the line equation:

$f(t) - 17.5 = -0.72 ( t - 1 ) \\ \\ f(t) = - 0.72t + 0.72 + 17.5 \\ \\ f(t) = -0.72t +18.22$

The linear function given above gives the percentage of high school students who drink and drive in year t, where t = 0 corresponds to year 2000.