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(1.7)x
f left parenthesis x right parenthesis equals 50 left parenthesis 1.7 right parenthesis superscript x baseline

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

Answer 1

To create an exponential function for a population of 50 insects growing at a rate of 7%, we start with the initial population and apply the growth rate.

1. The initial population is 50.
2. The growth rate is 7%, which means the growth factor is \(1 + 0.07 = 1.07\).

Thus, the function that represents the growth of the population over time \(x\) (where \(x\) is in the same time units as the growth rate) is:

\[ f(x) = 50(1.07)^x \]

Among the options provided, the correct function is:

f(x) = 50(1.07)^x.

This option accurately reflects the initial population and the exponential growth rate.