To determine the value [tex]\( V \)[/tex] of a machine at the end of 2 years given that the original cost [tex]\( C \)[/tex] was \[tex]$795 and the rate of depreciation \( r \) is 0.3, we will use the formula:
\[ V = C (1 - r)^t \]
Let's break down the solution step by step:
1. Identify the given values:
- Original cost, \( C = \$[/tex]795 \)
- Rate of depreciation, [tex]\( r = 0.3 \)[/tex]
- Number of years, [tex]\( t = 2 \)[/tex]
2. Substitute the given values into the formula:
[tex]\[
V = 795 \times (1 - 0.3)^2
\][/tex]
3. Perform the operations inside the parenthesis first:
[tex]\[
1 - 0.3 = 0.7
\][/tex]
4. Next, raise 0.7 to the power of 2:
[tex]\[
0.7^2 = 0.49
\][/tex]
5. Multiply this result by the original cost:
[tex]\[
V = 795 \times 0.49
\][/tex]
6. Calculate the multiplication:
[tex]\[
V = 389.55
\][/tex]
This is the value of the machine after 2 years.
7. Ensure the final value is rounded to the nearest cent, which in this case is:
[tex]\[
V = 389.55
\][/tex]
Thus, the value of the machine at the end of 2 years is \$389.55.
