Answer: 13 years.
Step-by-step explanation:
The price decreases by 14% anually
To find the decimal form, you have 14%/100% = 0.14
So, the year zero, the price is $27,500
After one year, the price is:
P = $27,500 - 0.14*$27500 = $27,500*(0.86)
After the second year, the price is:
P = $27,500*(0.86)^2
and so on, so we want to find x such that:
P = $27,500*(0.86)^x = $4000
0.86^x = $4000/$27,500
Now, using the natural logaritm rule:
a^x = b
x = ln(a)/ln(b)
x = ln($4000/$27,500)/ln(0.86) = 12.8
We can round it up to 13, so after 13 years the price of the car is about $4000
