The function \( g(x) = 11(1.2)^x \) models the insect population after \( x \) months. In this equation, the different components can be interpreted as follows:
- The constant \( 11 \): This represents the initial population of the insect before any time has passed (when \( x = 0 \)).
- The base \( 1.2 \): This value indicates the growth factor. Since it is greater than 1, it suggests that the population is increasing over time. Specifically, it implies that the population grows by 20% each month.
A good interpretation of one of the values in this function could be:
- The value \( 1.2 \) in the function indicates that the insect population increases by 20% each month. Thus, for each month that passes, the population will be multiplied by 1.2 compared to the previous month.
In summary, the best interpretation of the base \( 1.2 \) is that it represents the monthly growth rate of the insect population, showing that the population is expected to grow by 20% each month.