Question

Mr. Pickle bought an iPod from his friend who claims that the iPod was worth $250.00

when he bought it. The iPod's value decreases exponentially at the same rate each
year, and one year later the iPod's value is $187.50. By what percentage is the iPod's
value depreciating each year?

Answer 1

The iPod's value is depreciating by 25% each year, calculated using the exponential decay formula by comparing the initial value of $250.00 to the one-year value of $187.50.

Step-by-step explanation:

Mr. Pickle's iPod depreciates in value exponentially. After one year, the value decreased from $250.00 to $187.50. To find the annual depreciation percentage, we use the formula for exponential decay V = P(1 - r)^t, where V is the future value, P is the initial value, r is the rate of depreciation, and t is the time in years. In this case, we know the following:

• Initial value P = $250.00
• Value after one year V = $187.50
• Time t = 1 year

We can rearrange the equation to solve for r:

V = P(1 - r)^t
$187.50 = $250.00(1 - r)^1
0.75 = 1 - r
r = 1 - 0.75
r = 0.25

So the iPod's value is depreciating by 25% each year.