Answer :
To predict the purchasing power of \[tex]$20,000 ten years later using the equation
$[/tex][tex]$
y = 20000(0.95)^z,
$[/tex][tex]$
we set the number of years $[/tex]z = 10[tex]$. This gives:
$[/tex][tex]$
y = 20000(0.95)^{10}.
$[/tex][tex]$
Step 1. Calculate the decay factor over 10 years:
Compute
$[/tex][tex]$
(0.95)^{10} \approx 0.59874.
$[/tex][tex]$
This means the purchasing power retains about 59.874% of its initial value after 10 years.
Step 2. Multiply by the initial amount:
Now, multiply this factor by \$[/tex]20,000:
[tex]$$
y = 20000 \times 0.59874 \approx 11974.74.
$$[/tex]
Step 3. Rounding:
Rounding \[tex]$11974.74 to the nearest dollar gives approximately \$[/tex]11,975.
Thus, the purchasing power of \[tex]$20,000 ten years later is about \$[/tex]11,975.
$[/tex][tex]$
y = 20000(0.95)^z,
$[/tex][tex]$
we set the number of years $[/tex]z = 10[tex]$. This gives:
$[/tex][tex]$
y = 20000(0.95)^{10}.
$[/tex][tex]$
Step 1. Calculate the decay factor over 10 years:
Compute
$[/tex][tex]$
(0.95)^{10} \approx 0.59874.
$[/tex][tex]$
This means the purchasing power retains about 59.874% of its initial value after 10 years.
Step 2. Multiply by the initial amount:
Now, multiply this factor by \$[/tex]20,000:
[tex]$$
y = 20000 \times 0.59874 \approx 11974.74.
$$[/tex]
Step 3. Rounding:
Rounding \[tex]$11974.74 to the nearest dollar gives approximately \$[/tex]11,975.
Thus, the purchasing power of \[tex]$20,000 ten years later is about \$[/tex]11,975.
