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 Upper F left parenthesis x right parenthesis equals 0.629 x Superscript 1.482, where x is the number of years after 1940 and F(x) is the number of female researchers in thousands.
a. What type of function is this?
b. What is Upper F left parenthesis 30 right parenthesis? What does it mean?
c. How many female researchers will there be in 2020?
Question content area bottom
Part 1
a. Upper F left parenthesis x right parenthesis equals 0.629 x Superscript 1.482 is a
absolute value
function.
a. What type of function is this?
b. What is Upper F left parenthesis 30 right parenthesis? What does it mean?
c. How many female researchers will there be in 2020?
Question content area bottom
Part 1
a. Upper F left parenthesis x right parenthesis equals 0.629 x Superscript 1.482 is a
absolute value
function.
Answers
GPT-4o mini
a. The function \( F(x) = 0.629 x^{1.482} \) is a **power function** because it can be expressed in the form \( F(x) = ax^b \) where \( a = 0.629 \) and \( b = 1.482 \). It is not an absolute value function.
b. To find \( F(30) \):
\[
F(30) = 0.629 \times 30^{1.482}
\]
Calculating \( 30^{1.482} \):
\[
30^{1.482} \approx 37.408
\]
Now, substituting this into the equation:
\[
F(30) = 0.629 \times 37.408 \approx 23.5
\]
This means \( F(30) \approx 23.5 \), which indicates that there were approximately **23,500 female researchers** in the country 30 years after 1940 (i.e., in 1970).
c. To find the number of female researchers in 2020, we first determine how many years after 1940 that is:
\[
2020 - 1940 = 80 \quad \text{(so } x = 80\text{)}
\]
Now, we calculate \( F(80) \):
\[
F(80) = 0.629 \times 80^{1.482}
\]
Calculating \( 80^{1.482} \):
\[
80^{1.482} \approx 52.344
\]
Now, substituting this into the equation:
\[
F(80) = 0.629 \times 52.344 \approx 32.94
\]
This means \( F(80) \approx 32.94 \), indicating that there will be approximately **32,940 female researchers** in the country by the year 2020.
b. To find \( F(30) \):
\[
F(30) = 0.629 \times 30^{1.482}
\]
Calculating \( 30^{1.482} \):
\[
30^{1.482} \approx 37.408
\]
Now, substituting this into the equation:
\[
F(30) = 0.629 \times 37.408 \approx 23.5
\]
This means \( F(30) \approx 23.5 \), which indicates that there were approximately **23,500 female researchers** in the country 30 years after 1940 (i.e., in 1970).
c. To find the number of female researchers in 2020, we first determine how many years after 1940 that is:
\[
2020 - 1940 = 80 \quad \text{(so } x = 80\text{)}
\]
Now, we calculate \( F(80) \):
\[
F(80) = 0.629 \times 80^{1.482}
\]
Calculating \( 80^{1.482} \):
\[
80^{1.482} \approx 52.344
\]
Now, substituting this into the equation:
\[
F(80) = 0.629 \times 52.344 \approx 32.94
\]
This means \( F(80) \approx 32.94 \), indicating that there will be approximately **32,940 female researchers** in the country by the year 2020.