Question

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)

f(x)=50(1.7)^x

f(x)=50(0.07)^x

f(x)=50(1.07)^x

f(x)=50(0.93)^x

Answer 1

To represent a population of 50 insects growing at a rate of 7%, the correct exponential function should be in the form \( f(x) = P(1 + r)^x \), where \( P \) is the initial population, \( r \) is the growth rate (expressed as a decimal), and \( x \) is the time in appropriate units (e.g., years).

Given:
- Initial population, \( P = 50 \)
- Growth rate, \( r = 0.07 \) (which is 7%)

So, the function representing this growth will be:

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

Therefore, the accurate function is:

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