The scrap value of a machine at the end of its useful life is given by

​S(n)equals

​C(1minus​r)Superscript n

​,

where C is the original​ cost, n is the useful life of the machine in​ years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine.

Original​ cost,

​$52 comma 000

​;

​life,

6

​years; annual rate of value​ lost,

11

​%

Question content area bottom

Part 1

Sequals

​$enter your response here

​(Round to the nearest​ cent.)

To find the scrap value of the machine, we use the given formula:

\[ S(n) = C \times (1 - r)^n \]

Where:
- $ C $ is the original cost of the machine.
- $ r $ is the annual rate of value lost (as a decimal).
- $ n $ is the useful life of the machine in years.
- $ S(n) $ is the scrap value of the machine after $ n $ years.

Given:
- Original cost $ C = 52,000 $ dollars
- Life $ n = 6 $ years
- Annual rate of value lost $ r = 11\% = 0.11 $

Now, we can calculate the scrap value $ S(6) $:

\[
S(6) = 52,000 \times (1 - 0.11)^6
\]

Let's calculate this.The scrap value of the machine after 6 years is approximately \$25,843.03 (rounded to the nearest cent).

Would you like further details or have any questions? 

Here are 5 related questions to expand your understanding:
1. How would the scrap value change if the annual rate of value loss increased to 15%?
2. What would be the scrap value if the machine's life were 10 years instead of 6?
3. How is the formula derived for the scrap value of a machine?
4. How does compound depreciation compare to straight-line depreciation?
5. How would you calculate the original cost if you only knew the scrap value and depreciation rate?

**Tip:** When dealing with percentages in formulas, always convert the percentage to a decimal by dividing by 100.

The scrap value of a machine at the end of its useful life is given by S(n) = C(1 - r)^n, where C is the original cost, n is the useful life of the machine in years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine. Original cost: $52,000; life: 6 years; annual rate of value lost: 11%. Round to the nearest cent.

Learn how to calculate the scrap value of a machine using the exponential decay formula. This example includes an original cost of $52,000, 11% annual depreciation, and a 6-year lifespan, with a detailed step-by-step solution. Suitable for students in Grades 9-12.

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