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.

1 answer

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.
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