An insect population after x months can be modeled by the function "g" left parenthesis, "x" , right parenthesis equals 11 left parenthesis, 1.2 , right parenthesis Superscript, "x" , Baseline .

Question

gx=111.2x.Which statement is the best interpretation of one of the values in this function?

Answer 1

The function \( g(x) = 11(1.2)^x \) models the insect population after \( x \) months. In this function, there are two key components: the coefficient (11) and the base of the exponential term (1.2).

1. The Coefficient (11): This represents the initial population of the insects when \( x = 0 \). Specifically, when \( x = 0 \), \( g(0) = 11(1.2)^0 = 11 \). This means that the starting population of insects at the beginning (0 months) is 11.

2. The Base (1.2): This value indicates the growth factor of the population. The base of 1.2 means that the population increases by 20% each month. For every month that passes (each increment of \( x \)), the population is multiplied by 1.2.

Best Interpretation:

• The Initial Population: The value 11 in this function represents the initial population of the insect species at \( x = 0 \) months. It indicates that the population starts with 11 insects.

• The Growth Rate: The value 1.2 represents that the population grows by 20% each month.

So, a strong statement interpretation is:

"The initial population of the insect species is 11 insects when the observation starts."

Or,

"The insect population increases by 20% each month."

Both interpretations are significant and provide insight into the dynamics of the population modeled by the function.