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(0.93)x
f left parenthesis x right parenthesis equals 50 left parenthesis 0.93 right parenthesis superscript x baseline

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(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

Answer 1

To create an exponential function for the population of insects, we start with the initial population and then apply the growth rate.

Given:

• Initial population = 50 insects
• Growth rate = 7% = 0.07

The general formula for exponential growth is:

\[ f(x) = P_0 (1 + r)^x \]

where:

• \( P_0 \) is the initial population,
• \( r \) is the growth rate (as a decimal),
• \( x \) is the time in appropriate units (e.g., days, months, years).

Substituting the values into the formula, we get:

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

Thus, the correct function from the options provided is:

f(x) = 50(1.07)^x