00:01
So we have a car that starts off with the value of $38 ,000 in 2007, but by 2013, the car is now valued at $11 ,000.
00:09
And we want to know if it continues to depreciate at the same percentage rate, we want to know how much this car will be worth in 2017.
00:17
So we can set up an equation that looks like this.
00:19
F of x is equal to a, which is the principal amount that the car is worth, so $38 ,000, times b to the x minus 2007, as 2007 is a.
00:30
Our initial year.
00:31
We will need to subtract 2007 from whatever new year that we're in, whatever x new year that we're in, to get the amount of time that has passed since 2007.
00:42
So if we wanted to use the values of 11 ,000 and 2013, our 2013 would be plugged in for x and our 11 ,000 would be equal to f of x.
00:52
So we can write this equation to solve out for b by saying 11 ,000.
01:00
11 ,000 is equal to.
01:01
Equal to our value of a, which is 38 ,000, 38 ,000 times b, which is still some unknown value, times b, to the power of x 2013 minus 2007.
01:26
And 2013 minus 2007, we'll go ahead and simplify that in just a second if you end up doing that math.
01:33
It's just equal to six...