
Function Word Problem
A new set of car tires has a tread depth of 8 millimeters. The tread depth decreases 0.12 millimeters per thousand miles driven. Write an equation that gives the tread depth as a function of the distance driven. Then predict at what distance the tread depth will be 2 millimeters.
Thanks for any help.

Let's call the tread depth T, and the distance driven d. T as a function of d gives us:
$\displaystyle T(d)$
Note that the maximum tread depth is 8mm. Let's start with that:
T(d) = 8
However, it is stated that for every thousand miles driven, that number decreases by 0.12mm. This means that for every mile driven, the tread depth decreases by 0.00012mm. So our function becomes:
$\displaystyle
T(d) = 8  (0.00012d)$
Now, to find the distance where the tread depth is 2mm we simply have to use our new equation.
$\displaystyle
T(d) = 2$
Therefore:
$\displaystyle
2 = 8  (0.00012d)$
Now we just solve for $\displaystyle d$ to get:
$\displaystyle d = 50,000$
