Question

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 2 years if the original cost was $773 and r=0.3 .

Answer 1

The value of the machine at the end of 2 years, using the formula for depreciation, is calculated to be $378.77.

Step-by-step explanation:

The student has asked how to calculate the value of a machine at the end of two years, given the original cost and the rate of depreciation. This is a problem that involves exponential decay in the context of finance.

To find the value of the machine after two years, we'll use the 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, and r is the rate of depreciation. In this example, the original cost c is $773 and the rate of depreciation r is 0.3 or 30%.

Using these values, let's calculate:

1. First, subtract the depreciation rate from 1: 1 − 0.3 = 0.7.
2. Next, raise this result to the power of the number of years, which is 2: 0.7^2.
3. Now calculate the result of the raise power: 0.7^2 = 0.49.
4. Finally, multiply this result by the original cost to get the value of the machine: $773 × 0.49 = $378.77.

The value of the machine at the end of 2 years is $378.77.