Answer :
To solve this problem, we need to predict the future purchasing power of [tex]$20,000 using the equation \( y = 20000(0.95)^x \) after ten years.
Here's how we can break down the steps:
1. Understand the Equation: The equation \( y = 20000(0.95)^x \) represents the depreciation of the value of money over time. The starting amount is $[/tex]20,000, and it decreases by 5% each year (indicated by the factor 0.95, which is 1 - 0.05).
2. Identify the Variables: We need to find the value of [tex]\( y \)[/tex] (the future purchasing power) after 10 years. Here, [tex]\( x = 10 \)[/tex] because we are looking ten years into the future.
3. Substitute the Values: Plug [tex]\( x = 10 \)[/tex] into the equation:
[tex]\[
y = 20000 \times (0.95)^{10}
\][/tex]
4. Calculate [tex]\( (0.95)^{10} \)[/tex]: Raising 0.95 to the power of 10 will give us a decimal value that represents the purchasing power factor after ten years.
5. Multiply by the Initial Amount, [tex]\( 20000 \)[/tex]: Multiply this result by 20,000 to find the reduced purchasing power after 10 years.
After performing these calculations, the purchasing power of [tex]$20,000 after ten years is approximately $[/tex]11,975. This matches the option \[tex]$11,975 listed in the question.
Thus, the predicted purchasing power of $[/tex]20,000 ten years later is approximately \$11,975.
Here's how we can break down the steps:
1. Understand the Equation: The equation \( y = 20000(0.95)^x \) represents the depreciation of the value of money over time. The starting amount is $[/tex]20,000, and it decreases by 5% each year (indicated by the factor 0.95, which is 1 - 0.05).
2. Identify the Variables: We need to find the value of [tex]\( y \)[/tex] (the future purchasing power) after 10 years. Here, [tex]\( x = 10 \)[/tex] because we are looking ten years into the future.
3. Substitute the Values: Plug [tex]\( x = 10 \)[/tex] into the equation:
[tex]\[
y = 20000 \times (0.95)^{10}
\][/tex]
4. Calculate [tex]\( (0.95)^{10} \)[/tex]: Raising 0.95 to the power of 10 will give us a decimal value that represents the purchasing power factor after ten years.
5. Multiply by the Initial Amount, [tex]\( 20000 \)[/tex]: Multiply this result by 20,000 to find the reduced purchasing power after 10 years.
After performing these calculations, the purchasing power of [tex]$20,000 after ten years is approximately $[/tex]11,975. This matches the option \[tex]$11,975 listed in the question.
Thus, the predicted purchasing power of $[/tex]20,000 ten years later is approximately \$11,975.
