Question

Trevor bought a truck for $29,500. The value of the truck depreciates by 15% each year. Write an exponential function to represent the data and find the value of Trevor's truck in 6 years"

Answer 1

The exponential decay function for Trevor's truck's value with a 15% yearly depreciation is V = 29500(0.85)^t. Using this, after 6 years, the truck's predicted value is roughly $10,837.48.

Step-by-step explanation:

To determine the value of Trevor's truck after 6 years with an annual depreciation of 15%, we use an exponential decay function. The general formula of exponential decay is V = P(1 - r)^t, where V is the final value, P is the initial amount (principal), r is the rate of decay, and t is the time in years.

For Trevor's truck:

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The exponential function to represent the data is:

V = 29500(1 - 0.15)^t

To find the truck's value after 6 years:

V = 29500(1 - 0.15)^6

V = 29500(0.85)^6

V ≈ $10,837.48

After 6 years, Trevor's truck will approximately be valued at $10,837.48.