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.