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.