Question

The given function models the percentage, f(x), of people x years old with a certain disease. Evaluate f(81)="...and describe what this answer means in practical terms."

Answer 1

We have the following function:

`f(x)=(90)/(1+270e^(-0.122x))`

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:

`\begin{gathered} f(81)=(90)/(1+270e^(-0.122(81))) \\ \\ f(81)=(90)/(1+270(0.0000510860036217)) \\ \\ f(81)=88.7754999123 \end{gathered}`

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:

`f(81)\approx88.8\%\text{ }\rightarrow\text{ Rounded to one decimal place.}`

And

In practical terms, this means the following:

About 88.8% of 81-years-olds have the disease.