SOLUTION: A person bought a car for $21,049. After 3 years, the car was worth $11,980. If the value of the car continues to decrease exponentially at this rate, then determine the time it wi

Algebra ->  Finance -> SOLUTION: A person bought a car for $21,049. After 3 years, the car was worth $11,980. If the value of the car continues to decrease exponentially at this rate, then determine the time it wi      Log On


   

Question 1101146: A person bought a car for $21,049. After 3 years, the car was worth $11,980. If the value of the car continues to decrease exponentially at this rate, then determine the time it will take to be worth $5498
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
y=21049%2Ae%5E%28-k%2Ax%29

-

11980=21049%2Ae%5E%28-3k%29
11980%2F21049=e%5E%28-3k%29
0.569148=e%5E%28-3k%29
-0.5636148=-3k
k=0.5636148%2F3
k=0.1879

highlight%28y=21049%2Ae%5E%28-0.1879x%29%29


When will y=5498?
21049%2Ae%5E%28-0.1879x%29=5498

e%5E%28-0.1879x%29=0.261200
ln%28e%5E%28-0.1879x%29%29=-1.3425
-0.1879x=-1.3425

highlight_green%28x=7.144%29years
Close to 7 years 8 weeks.