marcysydnor17
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 $2968 and r=0.2. Round to the nearest cent.

Respuesta :

msm555

Answer:

$1215.69

Step-by-step explanation:

Given the formula for the value of a machine [tex]\sf V[/tex] at the end of [tex]\sf t[/tex] years:

[tex]\Large\boxed{\boxed{\sf V = C(1 - r)^t }}[/tex]

Where:

  • [tex]\sf C[/tex] is the original cost
  • [tex]\sf r[/tex] is the rate of depreciation
  • [tex]\sf t[/tex] is the number of years

We are given that [tex]\sf C = \$2968[/tex], [tex]\sf r = 0.2[/tex], and [tex]\sf t = 4[/tex].

We need to find the value of the machine at the end of 4 years.

Substituting the given values into the formula:

[tex]\sf V = 2968(1 - 0.2)^4 [/tex]

[tex]\sf V = 2968(0.8)^4 [/tex]

[tex]\sf V = 2968 \times 0.4096 [/tex]

[tex]\sf V = 1215.6928 [/tex]

[tex]\sf V = 1215.69 \textsf{(in nearest cent)}[/tex]

So, the value of the machine at the end of 4 years is approximately $1215.69.

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