A new car is purchased for $36000 and over it's value depreciates by 1/2 every five years. What is the value of the car 17 years after it was purchased to the nearest hundred dollar?

the value after 17 years is $3400

Step-by-step explanation:

We would apply the formula,

y = ab^t

Where

a represents the initial amount of the car.

t represents the depreciation time.

From the information given

a = 36000

t = 5 years

Since after 5 years, the value depreciates by 0.5, then

y = 0.5 × 36000 = 18000

Therefore

18000 = 36000 × b^5

Dividing through by 36000, it becomes

0.5 = b^5

Raising both sides of the equation by 1/5, it becomes

0.5^(1/5) = b^5/5

b = 0.871

The equation becomes

y = 36000(0.871)^t

After 17 years, the value of the car would be

y = 36000(0.871)^17

y = $3440

y = $3400 to the nearest hundred dollar

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step-by-step explanation: