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)

Question

Responses

f(x)=50(0.07)x
f left parenthesis x right parenthesis equals 50 left parenthesis 0.07 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(1.7)x

Answer 1

To represent a population of insects that is growing exponentially at a rate of 7%, the correct function can be derived from the general formula for exponential growth, which is:

\[ f(x) = P(1 + r)^x \]

where:

• \( P \) is the initial population (in this case, 50),
• \( r \) is the growth rate (in this case, 0.07 for 7%),
• \( x \) is the number of time periods (e.g., days, years, etc.).

Plugging in the values, we get:

\[ f(x) = 50(1 + 0.07)^x \] \[ f(x) = 50(1.07)^x \]

Thus, the correct function that represents the population of insects growing at a rate of 7% is:

f(x) = 50(1.07)^x

The corresponding option is:

f(x) = 50(1.07)^x (the third option).