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Answer :
To solve the problem of predicting the purchasing power of [tex]$20,000 after ten years, you can use the formula for exponential decay, which is typically used when dealing with depreciation or decreasing values over time. The provided equation is:
\[ y = 20000 \times (0.95)^{10} \]
Here's how you solve it step-by-step:
1. Initial Amount (Principal):
Start with the initial amount of money which is $[/tex]20,000.
2. Decay Rate (Depreciation Rate):
The decay rate given is 0.95, meaning the value decreases by 5% each year.
3. Time (Number of Years):
We want to find out the purchasing power after 10 years.
4. Applying the Formula:
Substitute the values into the equation:
[tex]\[ y = 20000 \times (0.95)^{10} \][/tex]
5. Calculate the Exponent:
First, calculate [tex]\((0.95)^{10}\)[/tex] by multiplying 0.95 by itself ten times. This represents the cumulative effect of a 5% reduction each year over ten years.
6. Final Calculation:
Multiply the initial amount by the result from the previous step:
[tex]\[ y = 20000 \times 0.59873694 \approx 11974.74 \][/tex]
By performing these calculations, the purchasing power of [tex]$20,000 after ten years is approximately $[/tex]11,974.74. Based on the given options, the closest answer is:
[tex]$11,975
So, the purchasing power of $[/tex]20,000 ten years later is approximately $11,975.
\[ y = 20000 \times (0.95)^{10} \]
Here's how you solve it step-by-step:
1. Initial Amount (Principal):
Start with the initial amount of money which is $[/tex]20,000.
2. Decay Rate (Depreciation Rate):
The decay rate given is 0.95, meaning the value decreases by 5% each year.
3. Time (Number of Years):
We want to find out the purchasing power after 10 years.
4. Applying the Formula:
Substitute the values into the equation:
[tex]\[ y = 20000 \times (0.95)^{10} \][/tex]
5. Calculate the Exponent:
First, calculate [tex]\((0.95)^{10}\)[/tex] by multiplying 0.95 by itself ten times. This represents the cumulative effect of a 5% reduction each year over ten years.
6. Final Calculation:
Multiply the initial amount by the result from the previous step:
[tex]\[ y = 20000 \times 0.59873694 \approx 11974.74 \][/tex]
By performing these calculations, the purchasing power of [tex]$20,000 after ten years is approximately $[/tex]11,974.74. Based on the given options, the closest answer is:
[tex]$11,975
So, the purchasing power of $[/tex]20,000 ten years later is approximately $11,975.
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