Question

The number of females in science continues to show steady increases. The number of female researchers in a certain country can be modeled by the function F(x)=0.742x1.353, where x is the number of years after 1950 and F(x) is the number of female researchers in thousands.a. What type of function is this?b. What is F(20)? What does it mean?c. How many female researchers will there be in 2040?

Answer 1

$f(x)=0.742x^{1.353}$

(a)

A function which is represented in the form:

$\begin{gathered} y=ax^b \\ where \\ a\in\R \\ b\in\R \end{gathered}$

It is a power function which is a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number.

(b)

$\begin{gathered} F(20)=0.742x^{1.353} \\ F(20)=0.742(20)^{1.353} \\ F(20)\approx42.727 \end{gathered}$

This represent the number of female researchers in thousands for the year 1970, or after 20 years.

(c)

$\begin{gathered} 2040,x=90 \\ F(90)=0.742(90)^{1.353} \\ F(90)=326.9595452 \\ F(90)\approx327 \\ ----- \\ F(90)=326960 \end{gathered}$