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 that represents a population of insects growing at a rate of 7%, we can use the formula:

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

where:

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

Given that the initial population, \( P_0 \), is 50 and the growth rate, \( r \), is 7% (which is 0.07 when expressed as a decimal), we can substitute these values into the formula:

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

Thus, the correct function representing the population is:

f(x) = 50(1.07)^x

This corresponds to the option:

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