contestada

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 $2106 and r=0.1 . Round to the nearest cent.

Respuesta :

sqdancefan

Answer:

  $1381.75

Step-by-step explanation:

You want the value of a $2106 machine after 4 years if it depreciates at 10% per year.

Formula

You are given the value formula ...

  V = C(1 -r)^t

with parameters C = 2106, r = 0.1, t = 4.

Put the numbers in the formula and do the arithmetic to find the value:

  V = 2106(1 -0.1)^4 ≈ 1381.75

The value of the machine after 4 years is about $1381.75.

Ver imagen sqdancefan
To find the value of the machine at the end of 4 years, we can use the given formula:

\[ V = C(1 - r)^t \]

Where:
- \( V \) is the value of the machine at the end of \( t \) years.
- \( C \) is the original cost of the machine.
- \( r \) is the rate of depreciation.
- \( t \) is the number of years.

Given that \( C = $2106 \), \( r = 0.1 \), and \( t = 4 \), we can plug these values into the formula:

\[ V = 2106(1 - 0.1)^4 \]

\[ V = 2106(0.9)^4 \]

Now, let's calculate:

\[ V = 2106(0.9)^4 \]
\[ V = 2106(0.6561) \]
\[ V ≈ 1380.6366 \]

Rounding to the nearest cent, the value of the machine at the end of 4 years is approximately $1380.64.

Otras preguntas