Questions: The value of a machine, V, at the end of t years is given by V=C(1-r)^t, where C is the original cost and r is the rate of depreciation. Find the value of a machine at the end of 4 years if the original cost was 2040 and r=0.1. Round to the nearest cent.

The value of a machine, V, at the end of t years is given by V=C(1-r)^t, where C is the original cost and r is the rate of depreciation. Find the value of a machine at the end of 4 years if the original cost was 2040 and r=0.1. Round to the nearest cent.

Transcript text: The value of a machine, $V$, at the end of $t$ years is given by $V=C(1-r)^{t}$, where $C$ is the original cost and $r$ is the rate of depreciation. Find the value of a machine at the end of 4 years if the original cost was $\$ 2040$ and $r=0.1$. Round to the nearest cent.

Solution

Solution Steps

Step 1: Identify the Parameters

The original cost of the machine, $C$, is $2040. The rate of depreciation, $r$, is 0.1. The time in years, $t$, is 4 years.

Step 2: Substitute the Parameters into the Formula

The formula to find the value of the machine at the end of $t$ years is $V=C(1-r)^{t}$.

Step 3: Calculate the Depreciation Factor

The depreciation factor, $(1-r)^{t}$, is calculated as $(1-0.1)^{4} = 0.656$.

Step 4: Calculate the Value of the Machine

The value of the machine, $V$, is calculated as $2040 \times 0.656 = $1338.44$.

Final Answer:

The value of the machine at the end of 4 years, rounded to 2 decimal places, is $1338.44.

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