Answer :
To predict the purchasing power of [tex]$20,000 after ten years using the equation \( y = 20000(0.95)^x \):
1. Identify the components of the equation:
- The initial amount (purchasing power now) is $[/tex]20,000.
- The decay rate (0.95) represents a 5% decrease each year, indicating that the purchasing power reduces by 5% every year.
- [tex]\( x \)[/tex] is the number of years, and in this case, it is 10 years.
2. Apply the values to the equation:
- Substitute the values into the equation:
[tex]\[
y = 20000 \times (0.95)^{10}
\][/tex]
3. Calculate the result step-by-step:
- First, find [tex]\( (0.95)^{10} \)[/tex]. This calculates the effect of the 5% decrease over 10 years.
- Multiply the result by the initial amount, [tex]$20,000.
4. Find the purchasing power:
- After performing the calculation, the predicted purchasing power of $[/tex]20,000 after ten years is approximately \[tex]$11,975.
So, the purchasing power after ten years is $[/tex]11,975.
1. Identify the components of the equation:
- The initial amount (purchasing power now) is $[/tex]20,000.
- The decay rate (0.95) represents a 5% decrease each year, indicating that the purchasing power reduces by 5% every year.
- [tex]\( x \)[/tex] is the number of years, and in this case, it is 10 years.
2. Apply the values to the equation:
- Substitute the values into the equation:
[tex]\[
y = 20000 \times (0.95)^{10}
\][/tex]
3. Calculate the result step-by-step:
- First, find [tex]\( (0.95)^{10} \)[/tex]. This calculates the effect of the 5% decrease over 10 years.
- Multiply the result by the initial amount, [tex]$20,000.
4. Find the purchasing power:
- After performing the calculation, the predicted purchasing power of $[/tex]20,000 after ten years is approximately \[tex]$11,975.
So, the purchasing power after ten years is $[/tex]11,975.
