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 $718 and r=0.2.  Round to the nearest cent.

The formula for the value of a machine at the end of $ t $ years is:

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

Where:
- $ C $ is the original cost,
- $ r $ is the rate of depreciation, and
- $ t $ is the time in years.

Given:
- $ C = 718 $,
- $ r = 0.2 $,
- $ t = 4 $.

Substitute the values into the formula:

\[
V = 718(1 - 0.2)^4
\]

Simplifying the expression:

\[
V = 718(0.8)^4
\]

Now, let's calculate $ (0.8)^4 $ and then multiply by 718 to find the value of the machine.The value of the machine at the end of 4 years is approximately $294.09.

Would you like further details on the steps or have any questions?

Here are 5 related questions to explore further:
1. What would the value be after 6 years?
2. How does the depreciation rate affect the machine's value over time?
3. What happens to the value if the depreciation rate is increased to 0.3?
4. How would you calculate the time required for the machine's value to drop below $100?
5. How would a compound interest formula differ from this depreciation model?

**Tip:** Exponential decay models, like the one used here, describe processes where quantities decrease by a constant percentage each period.

Find the value of a machine at the end of 4 years if the original cost was $718 and the rate of depreciation is 0.2. Round to the nearest cent.

Learn how to calculate the depreciation value of a machine after 4 years with a 20% annual depreciation rate. Using the exponential decay formula V = C(1 - r)^t, we find the value for an initial cost of $718. This example is perfect for students studying exponential decay in Grades 9-12.

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