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(0.07)^x
f left parenthesis x right parenthesis equals 50 left parenthesis 0.07 right parenthesis superscript x baseline

f(x)=50(1.07)^x

Answer 1

To create an exponential function representing a population of 50 insects that is growing at a rate of 7%, we can use the formula:

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

where:

• \( P_0 \) is the initial population (50 insects in this case),
• \( r \) is the growth rate (7% or 0.07),
• \( x \) is the time in appropriate units (e.g., days, months).

Plugging in the values:

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

Thus, the correct function from your options is:

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

So the accurate response is:

f(x)=50(1.07)^x