Part 2 of The Series: Exponents
Algebra
Level
2
Riley just read that her computer, which costs $2,400 new, loses 10% of its value every year. If this estimate is accurate, how much will the computer be worth in 2 years?
If necessary, round your answer to the nearest cent.
$78.00
$850.33
$1,002.50
$1944.00
$250.33
$1,000.50
$999.50
$600.50
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1 solution
The formula for exponential decay is
y = a(1 – r)^t
where a is the initial amount, r is the rate of decrease expressed as a decimal, t is the time elapsed, and y is the final amount.
Plug in $2,400 for the initial amount, 0.1 for the rate of decrease, and 2 years for the time elapsed.
y = a(1 – r)t
y = 2,400(1 – 0.1)2 Plug in
y = 2,400(0.9)2 Subtract
y = 2,400(0.81) Simplify
y = 1,944 Multiply
In 2 years, the computer will be worth $1,944.00.