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

f(x)=50(0.93)x

Answer 1

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

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

where:

• \( P_0 \) is the initial population (50 insects),
• \( r \) is the growth rate (7% = 0.07),
• \( x \) is the time (in whatever units you are measuring).

Using these values, we can substitute into the formula:

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

The correct function is:

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

So the accurate response from the provided options is:

f(x) = 50(1.07)^x