SOLUTION: A person bought a cat for $21,028. After 4 years, the car was worth $11,987. If the value of the car continues to decrease exponentially at this rate then determine the time it wil

Algebra ->  Finance -> SOLUTION: A person bought a cat for $21,028. After 4 years, the car was worth $11,987. If the value of the car continues to decrease exponentially at this rate then determine the time it wil      Log On


   

Question 1101259: A person bought a cat for $21,028. After 4 years, the car was worth $11,987. If the value of the car continues to decrease exponentially at this rate then determine the time it will take to be worth $4992
Found 2 solutions by jorel1380, richwmiller:
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
If the value decreases exponentially, then:
11987=21028e^-4k; where k is the depreciation constant. So
.57005=e^-4k
ln .57005=5ln e^-4k=-4k ln e=-4k
k=0.140508
Then:
4992/21028=e^-0.140508t
ln 0.2374=ln e^-0.140508t=-0.140508t ln e=-0.140508t
t=10.234 years for the car to be worth $4992
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Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
"A person bought a cat for $21,028."
Very expensive cat but a decent price for a car.