# Function Word Problem

Printable View

• Feb 11th 2008, 07:11 PM
Averee
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.
• Feb 11th 2008, 07:29 PM
topher0805
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\$
• Feb 12th 2008, 04:42 AM
Averee
Thanks a lot (Rofl)