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The value of a machine, [tex]\( V \)[/tex], at the end of [tex]\( t \)[/tex] years is given by [tex]\( V = C(1 - r)^t \)[/tex], where [tex]\( C \)[/tex] is the original cost and [tex]\( r \)[/tex] is the rate of depreciation.

Find the value of a machine at the end of 4 years if the original cost was [tex]\( \$2838 \)[/tex] and [tex]\( r = 0.2 \)[/tex]. Round to the nearest cent.



Answer :

GinnyAnswer
To find the value of the machine after 4 years given that the original cost is [tex]$2838 and the depreciation rate is 0.2 (or 20%), we can follow these steps: 1. Identify the given variables: - \( C \) (original cost) = $[/tex]2838
- [tex]\( r \)[/tex] (rate of depreciation) = 0.2
- [tex]\( t \)[/tex] (time in years) = 4

2. Substitute these values into the depreciation formula:
[tex]\[ V = C(1 - r)^t \][/tex]
Here,
[tex]\[ V = 2838 \cdot (1 - 0.2)^4 \][/tex]

3. Simplify the expression inside the parentheses:
[tex]\[ 1 - 0.2 = 0.8 \][/tex]
So the formula becomes:
[tex]\[ V = 2838 \cdot (0.8)^4 \][/tex]

4. Calculate [tex]\((0.8)^4\)[/tex]:
[tex]\[ 0.8^4 = 0.4096 \][/tex]

5. Multiply the original cost by this value:
[tex]\[ V = 2838 \cdot 0.4096 \][/tex]

6. Perform the multiplication:
[tex]\[ 2838 \cdot 0.4096 = 1162.4448 \][/tex]

7. Round the result to the nearest cent:
[tex]\[ 1162.4448 \approx 1162.44 \][/tex]

So, the value of the machine at the end of 4 years is [tex]\( \boxed{1162.44} \)[/tex] dollars.