QuestionJuly 15, 2025

A car purchased new for 30,000 depreciates at a rate of 12% per year. Fill in the missing part of the equation. (2 points) A(t)=30,000 square ^5 What is the value after 5 years?You do not need a dollar sign for your answer. Round to the nearest cent. (1 point) A(5)= square

A car purchased new for 30,000 depreciates at a rate of 12% per year. Fill in the missing part of the equation. (2 points) A(t)=30,000 square ^5 What is the value after 5 years?You do not need a dollar sign for your answer. Round to the nearest cent. (1 point) A(5)= square
A car purchased new for 30,000 depreciates at a rate of 12%  per year. Fill in the missing part of the equation. (2 points)
A(t)=30,000 square ^5
What is the value after 5 years?You do not need a dollar sign for your answer. Round to the nearest cent. (1 point)
A(5)= square

Solution
4.4(380 votes)

Answer

15,831.93 Explanation 1. Identify the depreciation formula The formula for depreciation is A(t) = P(1 - r)^t, where P is the initial value, r is the rate of depreciation, and t is time in years. 2. Fill in the missing part of the equation Given P = 30,000, r = 0.12, and t = 5, substitute into the formula: A(t) = 30,000(1 - 0.12)^5. 3. Calculate the value after 5 years Compute A(5) = 30,000 \times (0.88)^5. 4. Perform the calculation A(5) = 30,000 \times 0.527731 = 15,831.93.

Explanation

1. Identify the depreciation formula<br /> The formula for depreciation is $A(t) = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of depreciation, and $t$ is time in years.<br /><br />2. Fill in the missing part of the equation<br /> Given $P = 30,000$, $r = 0.12$, and $t = 5$, substitute into the formula: $A(t) = 30,000(1 - 0.12)^5$.<br /><br />3. Calculate the value after 5 years<br /> Compute $A(5) = 30,000 \times (0.88)^5$. <br /><br />4. Perform the calculation<br /> $A(5) = 30,000 \times 0.527731 = 15,831.93$.
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