A rule-of-thumb used by car dealers is that the trade-in value of a car decreases by 20% of its value each year. Homework Help ✎
Explain how the phrase “decreases by 20% of its value each year” tells you that the trade-in value varies exponentially with time (i.e., can be represented by an exponential function).
Suppose the initial value of your car is $23,500. Write an equation expressing the trade-in value of your car as a function of the number of years from now.
How much will your car be worth in four years?
In how many years will the trade-in value of your car be $6000?
If your car is really 2.7 years old now, what was its trade-in value when it was new?
'Decreases by 20%' means that you multiply by 0.8 each year. A sequence with a multiplier is geometric and has an exponential rule.
y = 23500(0.8)x
Use the equation that you found in part (b).
6000 = 23500(0.8)x
Divide by 23,500 first then take the log of both sides.
You are solving for A, which is 23,500 in part (b). The current price will be $23,500, and x will be 2.7.
Your answer should be larger than $23,500.