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The depreciation of a car can be modeled by the equation y = 26,600(1 - 0.055)ᵗ. What will be the value of the car in 5 years?

a. $15,090
b. $17,281
c. $18,238
d. $19,586

User Jiexi
by
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1 Answer

4 votes

Final answer:

To find the car's value after 5 years using the provided depreciation formula, plug in t = 5, calculate the depreciation factor (0.945^5), and multiply the result by the initial value of the car. The closest answer to our calculation (20,045.76) from the provided options is d. $19,586.

Step-by-step explanation:

The question asks to calculate the value of a car after 5 years based on a given depreciation equation. The student should use the provided formula y = 26,600(1 - 0.055)ᵢ and plug in t = 5 to find the car's value after 5 years. Here's how you calculate it:

y = 26,600(1 - 0.055)⁵

First, calculate the depreciation factor: (1 - 0.055) = 0.945

Then take that value to the power of 5: 0.945⁵

0.945⁵ ≈ 0.7536

Finally, multiply this factor by the initial value of the car:

y ≈ 26,600 * 0.7536 ≈ 20,045.76

The answer is not exactly one of the provided options, but the value closest to our result is option d. $19,586.

User Dgel
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