SOLUTION: A car has a purchase price of $23,500. The value declines continuously at an exponential rate of 27% annually. a. What is an equation modeling the value of this car after "t" y

Algebra ->  Finance -> SOLUTION: A car has a purchase price of $23,500. The value declines continuously at an exponential rate of 27% annually. a. What is an equation modeling the value of this car after "t" y      Log On


   



Question 1005053: A car has a purchase price of $23,500. The value declines continuously at an exponential rate of 27% annually.
a. What is an equation modeling the value of this car after "t" years?
b. What is the value after 5 years?
c. How long will it take for its value to be $2000?

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
v=23500%280.73%29%5Et




log%2810%2Cv%29=log%2810%2C23500%29%2Bt%2Alog%2810%2C0.73%29

t%2Alog%2810%2C0.73%29=log%2810%2C%282000%2F23500%29%29

t=log%2810%2C%282000%2F23500%29%29%2Flog%2810%2C0.73%29


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(b)
Let t=5

(c)
I just did part (c).

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A car has a purchase price of $23,500. The value declines continuously at an exponential rate of 27% annually.
a. What is an equation modeling the value of this car after "t" years?
b. What is the value after 5 years?
c. How long will it take for its value to be $2000?
Equation for value of car after "t" years: highlight_green%28V%28t%29+=+23500e%5E%28-+0.27t%29%29
Value of car after 5 years: highlight_green%28V%285%29+=+23500e%5E%28-+0.27%285%29%29%29. Calculate V(5)
Time it'll take for value to be $2,000: highlight_green%282000+=+23500e%5E%28-+0.27t%29%29. Calculate "t."