QuestionAugust 20, 2025

2. A computer valued at 6500 depreciates at the rate of 14.3% per year. a. Write a function that models the value of the computer. b. Find the value of the computer after three years.

2. A computer valued at 6500 depreciates at the rate of 14.3% per year. a. Write a function that models the value of the computer. b. Find the value of the computer after three years.
2. A computer valued at 6500 depreciates at the rate of 14.3% per year. a. Write a function that models the value of the computer. b. Find the value of the computer after three years.

Solution
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Answer

The value of the computer after three years is approximately \ 4090.50. Explanation 1. Write the depreciation function The value of the computer depreciates exponentially. Use the formula for exponential decay: **V(t) = V_0 \times (1 - r)^t**, where V_0 is the initial value, r is the rate of depreciation, and t is time in years. 2. Substitute values into the function Here, V_0 = 6500, r = 0.143. So, the function becomes V(t) = 6500 \times (1 - 0.143)^t. 3. Calculate the value after three years Substitute t = 3 into the function: V(3) = 6500 \times (1 - 0.143)^3. 4. Perform the calculation Calculate V(3) = 6500 \times 0.857^3 = 6500 \times 0.629.

Explanation

1. Write the depreciation function<br /> The value of the computer depreciates exponentially. Use the formula for exponential decay: **$V(t) = V_0 \times (1 - r)^t$**, where $V_0$ is the initial value, $r$ is the rate of depreciation, and $t$ is time in years.<br /><br />2. Substitute values into the function<br /> Here, $V_0 = 6500$, $r = 0.143$. So, the function becomes $V(t) = 6500 \times (1 - 0.143)^t$.<br /><br />3. Calculate the value after three years<br /> Substitute $t = 3$ into the function: $V(3) = 6500 \times (1 - 0.143)^3$.<br /><br />4. Perform the calculation<br /> Calculate $V(3) = 6500 \times 0.857^3 = 6500 \times 0.629$.
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