Question

Upper F left parenthesis x right parenthesis equals 0.718 x Superscript 1.412 is a
power
function.
Part 2
b. Upper F left parenthesis 35 right parenthesisequals
  
108.730
​(Round to the nearest thousandth as​ needed.)
Part 3
This means there were
  
478,767 female engineers in the year
  
2040.

Answer 1

To solve this, let's break down the information provided step by step.

1. **Understanding the power function**: The function you provided is \( F(x) = 0.718 \cdot x^{1.412} \). This is indeed a power function, where \( 0.718 \) is a coefficient and \( 1.412 \) is the exponent.

2. **Calculating \( F(35) \)**: You've mentioned that \( F(35) = 108.730 \). This means that substituting \( x = 35 \) into the function results in a value of approximately \( 108.730 \), as follows:

\[
F(35) = 0.718 \cdot 35^{1.412}
\]

Performing that calculation would yield the result of approximately \( 108.730 \), rounded to the nearest thousandth.

3. **Interpreting the result**: According to your statement, this calculation indicates that there were approximately 478,767 female engineers in the year 2040.

To finish this, the information can be summarized as follows:

- The function \( F(x) = 0.718 \cdot x^{1.412} \) gives a prediction of a certain quantity (in this case, possibly the number of engineers).
- When \( x = 35 \), the value of \( F(35) \) is approximately \( 108.730 \).
- Using this function model, projections suggest that there will be approximately **478,767** female engineers in the year **2040**.