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A fully loaded Toyota Forerunner sells for $42,000. It depreciates 12% per year from the date of purchase. How many years will it take to be worth half its value?

A fully loaded Toyota Forerunner sells for $42,000. It depreciates 12% per year from-example-1
User Ebaynaud
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1 Answer

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Answer:

Step-by-step explanation:

The formula for calculating exponential decay is expressed as

A = P(1 - r)^t

where

A is the price after t years

P is the initial price

r is the rate of decay

t is the number of years

From the information given

P = 42000

r - 12% = 12/100 = 0.12

By the time it is half of its initial price, A = 42000/2 = 21000

By substituting these values into the formula, we have

21000 = 42000(1 - 0.12)^t

21000/42000 = (0.88)^t

0.5 = (0.88)^t

Taking natural log of both sides,

ln 0.5 = tln0.88

t = ln0.5/ln0.88

t = 5.44

The closest option is 6

Thus,

time = 6 years

User Collin M
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