SOLUTION: The value of a new car depreciates at a rate of 34% each year from the year it is driven off the lot of the dealership. If the value of the car was $33,000 the year it was bought,

Question 721371: The value of a new car depreciates at a rate of 34% each year from the year it is driven off the lot of the dealership. If the value of the car was $33,000 the year it was bought, how long will it be until the car is worth only $4,000.
Write an exponential model for the value of the car, V(t), in dollars, as a function of time, t, years since the car was purchased. b) Determine the year in which the value of the car isworth only $2000. Set up the equation to be solved then solve this using logarithm. You can check your solution graphically. Round to two decimals
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The value of a new car depreciates at a rate of 34% each year from the year it is driven off the lot of the dealership.
a) If the value of the car was $33,000 the year it was bought,
How long will it be until the car is worth only $4,000.
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Write an exponential model for the value of the car, V(t), in dollars, as a function of time, t, years since the car was purchased.
V(t) = 33,000(0.66)^t
Solve for "t":
33,000(0.66)^t = 4000
0.66^t = 4/33
Take the log:
t = log(4/33)/log(0.66)
t = 5.08 years
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b) Determine the year in which the value of the car is worth only $2000. Set up the equation to be solved then solve this using logarithm. You can check your solution graphically. Round to two decimals
33,000(0.66)^t = 2000
0.66^t = 2/33
t = log(2/33)/log(0.66)
t = 6.737
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Cheers,
Stan H.
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