We have the following function:
[tex]f(x)=\frac{90}{1+270e^{-0.122x}}[/tex]
And we already know that:
• The function, f(x), models the percentage of people x years old with a certain disease.
And we need to evaluate the function for x = 81.
1. Therefore, to evaluate the function, we need to know that:
• The function will give us a percentage.
,
• We will evaluate the function of people aging 81 years old since x = 81 (81 years old).
2. Then we have to substitute the value x = 81. Then we have - using a graphing calculator:
[tex]\begin{gathered} f(81)=\frac{90}{1+270e^{-0.122(81)}} \\ \\ f(81)=\frac{90}{1+270(0.0000510860036217)} \\ \\ f(81)=88.7754999123 \end{gathered}[/tex]
3. Then the answer is 88.775...percent of people (81 years old). If we round our result to one decimal place, we have that f(81) = 88.8%
Therefore, in summary, we can conclude that:
[tex]f(81)\approx88.8\%\text{ }\rightarrow\text{ Rounded to one decimal place.}[/tex]
And
In practical terms, this means the following:
About 88.8% of 81-years-olds have the disease.
