Certainly! Let's solve this problem step by step.
### Problem Statement
We are given a mathematical model that predicts the percentage, [tex]\( R \)[/tex], of Americans who are retired in a given year [tex]\( t \)[/tex]. The model is expressed by the formula:
[tex]\[
R = \frac{t}{588.24} - 3.24
\][/tex]
Here, [tex]\( R \)[/tex] is the percentage of retired people (expressed as a decimal), and [tex]\( t \)[/tex] is the year.
### Given Year: 2016
We are specifically asked about the year 2016. In this context, [tex]\( t = 2016 \)[/tex].
### Step-by-Step Solution:
1. Substitute [tex]\( t \)[/tex] with 2016 in the equation:
[tex]\[
R = \frac{2016}{588.24} - 3.24
\][/tex]
2. Perform the division:
Calculate [tex]\( \frac{2016}{588.24} \)[/tex]:
[tex]\[
\frac{2016}{588.24} \approx 3.426
\][/tex]
3. Subtract 3.24 from the result:
[tex]\[
R = 3.426 - 3.24
\][/tex]
4. Complete the subtraction:
[tex]\[
R = 0.186
\][/tex]
### Final Answer
When [tex]\( t = 2016 \)[/tex], the percentage of Americans who are retired, according to the model, is approximately [tex]\( 0.186 \)[/tex] or 18.6%.
To summarize:
In the year 2016, the model predicts that approximately 18.6% of Americans are retired.
