Question

Im really confused, can someone answer/explain?

Answer 1

Answer:

0<=x<10 or [1,10)

Step-by-step 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)