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. Round to the nearest cent.

Answer 1

The value of the machine after 2 years is calculated using the formula V=C(1-r)^t with C=$773, r=0.3, and t=2, resulting in a value of $378.77.

Step-by-step explanation:

To solve the mathematical problem completely regarding the value of a machine after 2 years, we'll apply the given formula V = C(1 - r)^t. In this problem, C represents the original cost of the machine, which is $773, and r represents the rate of depreciation, which is given as 0.3. The variable t represents the number of years, which is 2 in this case.

The calculation steps are as follows:

Start with the original value of the machine, which is $773.

Determine the depreciation rate, which is 0.3.

Calculate the value after 2 years by raising (1 - 0.3) to the power of 2, which is (1 - 0.3)^2 or 0.7^2.

Multiply the initial value $773 by 0.7^2 to find the value at the end of 2 years.

Performing the calculation:

(1 - 0.3)^2 = 0.7^2 = 0.49

V = 773 × 0.49 = $378.77 (after rounding to the nearest cent).

Thus, the value of the machine at the end of 2 years, given a 30% depreciation rate, is $378.77.