Question
Exponential Functions in Context Quick Check
1 of 51 of 5 Items
Question
Create an exponential function to represent a population of 50 insects that is growing at a rate of 7%. Which of the following functions is accurate?(1 point)
Responses
f(x)=50(1.7)x
f left parenthesis x right parenthesis equals 50 left parenthesis 1.7 right parenthesis superscript x baseline
f(x)=50(0.93)x
f left parenthesis x right parenthesis equals 50 left parenthesis 0.93 right parenthesis superscript x baseline
f(x)=50(1.07)x
f left parenthesis x right parenthesis equals 50 left parenthesis 1.07 right parenthesis superscript x baseline
f(x)=50(0.07)x
Answers
GPT-4o mini
To model the exponential growth of a population of insects that starts at 50 and grows at a rate of 7%, the correct exponential function to represent this situation is:
\[ f(x) = 50(1.07)^x \]
Here’s why:
- The initial population is 50, which is the starting value.
- A growth rate of 7% translates to a growth factor of \( 1 + 0.07 = 1.07 \).
- The variable \( x \) typically represents time in units of your choice (e.g., days, months, years).
Thus, the accurate function is:
**f(x) = 50(1.07)^x**
\[ f(x) = 50(1.07)^x \]
Here’s why:
- The initial population is 50, which is the starting value.
- A growth rate of 7% translates to a growth factor of \( 1 + 0.07 = 1.07 \).
- The variable \( x \) typically represents time in units of your choice (e.g., days, months, years).
Thus, the accurate function is:
**f(x) = 50(1.07)^x**