Question
An insect population after x months can be modeled by the function `g\left(x\right)=11\left(1.2\right)^{x}.`Which statement is the best interpretation of one of the values in this function?
Answers
GPT-4o mini
The function \( g(x) = 11(1.2)^x \) models the population of an insect species after \( x \) months.
To interpret the components of this function:
1. **The value of 11**: This represents the initial insect population when \( x = 0 \) months. Therefore, \( g(0) = 11(1.2)^0 = 11 \). This means the initial population of the insects is 11.
2. **The base \( 1.2 \)**: This indicates the growth factor of the insect population per month. Since the base is greater than 1, it suggests that the population is growing. Specifically, a value of 1.2 means that each month, the insect population increases by 20%.
So the best interpretation of **one of the values in this function** is:
- **The initial population of the insects is 11.**
- Alternatively, **The population of the insects increases by 20% each month.**
Which interpretation to choose depends on the context, but either statement accurately captures an important aspect of the function.
To interpret the components of this function:
1. **The value of 11**: This represents the initial insect population when \( x = 0 \) months. Therefore, \( g(0) = 11(1.2)^0 = 11 \). This means the initial population of the insects is 11.
2. **The base \( 1.2 \)**: This indicates the growth factor of the insect population per month. Since the base is greater than 1, it suggests that the population is growing. Specifically, a value of 1.2 means that each month, the insect population increases by 20%.
So the best interpretation of **one of the values in this function** is:
- **The initial population of the insects is 11.**
- Alternatively, **The population of the insects increases by 20% each month.**
Which interpretation to choose depends on the context, but either statement accurately captures an important aspect of the function.