Answer:
0<=x<10 or [1,10)
Explanation:
You need to solve this using logarithms. I will use natural logarithms (LN on your calculator)
15,000 is the initial price of the car because 0.88^0=1.
All we need is 0.88^x>0.1
Remember that the logarithm of a^b is b*LN(a).
x*LN(0.88)>LN(0.1)
x<LN(0.1)/LN(0.88)
The relation changes from > to < because we are dividing by LN(0.88) which is negative.
The calculator now yields
LN(0.1)/LN(0.88)=10
So, x<10 years. But you buy the car at x=0, hence the relevant domain is.
0<=x<10 or [1,10)