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A new sports car sells for $40,000. The value of the car decreases by 12% annually. After how many years will it be worth half of its selling price

User Erikvimz
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1 Answer

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Final answer:

To find out after how many years the value of the car will be worth half of its selling price, we can set up an equation using exponential decay. After solving the equation, we find that it will take approximately 4.81 years for the car to be worth half of its selling price.

Step-by-step explanation:

To find out after how many years the value of the car will be worth half of its selling price, we can set up an equation using exponential decay.

Let y be the value of the car after t years. The equation would be y = 40000 * (1 - 0.12)^t.

We want to find t when y = 20000.

20000 = 40000 * (1 - 0.12)^t

0.5 = 0.88^t

Take the logarithm of both sides:

log(0.5) = log(0.88^t)

log(0.5) = t * log(0.88)

t = log(0.5) / log(0.88)

Using a calculator, we find t ≈ 4.81 years.

Therefore, it will take approximately 4.81 years for the car to be worth half of its selling price.

User Vincent
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