A new car sells for $27,500. The value of the car decreases by 14% annually. You want to sell the car when it's worth about $4000. Explain how many years you will keep the car, when you will sell it, and how you determined your answer. Pleas some one please help me explain ever step pleas i have to tell my teacher how i got my answer please.

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