Thread: 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:



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:



Now, to find the distance where the tread depth is 2mm we simply have to use our new equation.


Therefore:



Now we just solve for to get:

Thanks a lot