A certain type of car depreciates at a rate of 20% per year. If the car is currently worth $15,000, what will its value be after 2 years?
1. Identify the formula for exponential decay:
The formula for exponential decay in the context of depreciation is , where:
is the final amount (the value of the car after years).
is the initial amount (the initial value of the car), here = $.
is the rate of decay as a decimal. Given a depreciation rate of , so .
is the number of years, here .
2. Substitute the values into the formula:
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