Question

the number of females in medicine continues to show steady increases. the number of female physicians in a certain country can be modeled by the function ( f(x)=0.673x^{1.211} ) where ( x ) is the number of years after 1970 and ( f(x) ) is the number of female physicians in thousands

a. what type of function is this?
b. what is ( f(30) )? what does it mean?
c. how many female physicians will there be in 2040?

a. ( f(x)=0.673x^{1.211} ) is a power function.
b. ( f(30)=41.382 ) (round to the nearest thousandth as needed.)
this means there were ( square ) female physicians in the year ( square ) (round to the nearest whole number as needed.)

Explanation:

Step1: Calculate \(F(30)\)

Given \(F(x) = 0.673x^{1.211}\), substitute \(x = 30\) into the function:

$$F(30)=0.673\times30^{1.211}$$

First, calculate \(30^{1.211}\). Using a calculator, \(30^{1.211}\approx61.206\)
Then, \(F(30)=0.673\times61.206\approx41.382\)

Step2: Interpret the result

Since \(x\) is the number of years after 1970, when \(x = 30\), the year is \(1970 + 30=2000\). And \(F(x)\) is the number of female physicians in thousands. So when \(F(30)\approx41.382\), rounding to the nearest whole number, the number of female physicians is \(41\) (in thousands).

Answer:

\(F(30)\approx41.382\). This means there were \(41\) (in thousands) female physicians in the year \(2000\)