Question
An insect population after x months can be modeled by the function g(x) =18(1.3)^x
. Which statement is the best interpretation of one of the values in this function?
Question 2 options:
The insect population increased by 13 insects each month
The insect population increased at a rate of 30% each month
The insect population decreased at a rate of 30% each month
. Which statement is the best interpretation of one of the values in this function?
Question 2 options:
The insect population increased by 13 insects each month
The insect population increased at a rate of 30% each month
The insect population decreased at a rate of 30% each month
Answers
GPT-4o mini
To interpret the function \( g(x) = 18(1.3)^x \), let's break down the components:
- The initial value (when \( x = 0 \)) is \( g(0) = 18(1.3)^0 = 18 \). This means the initial population of insects is 18.
- The term \( (1.3)^x \) indicates that for each month that passes (each increase in \( x \)), the population is multiplied by 1.3, which represents a growth factor.
The growth factor of 1.3 indicates that the insect population increases by 30% each month, since:
- A growth factor greater than 1 indicates an increase (in this case, \( 1.3 - 1 = 0.3 \) or 30%).
Based on this analysis, the best interpretation of one of the values in this function is:
**The insect population increased at a rate of 30% each month.**
- The initial value (when \( x = 0 \)) is \( g(0) = 18(1.3)^0 = 18 \). This means the initial population of insects is 18.
- The term \( (1.3)^x \) indicates that for each month that passes (each increase in \( x \)), the population is multiplied by 1.3, which represents a growth factor.
The growth factor of 1.3 indicates that the insect population increases by 30% each month, since:
- A growth factor greater than 1 indicates an increase (in this case, \( 1.3 - 1 = 0.3 \) or 30%).
Based on this analysis, the best interpretation of one of the values in this function is:
**The insect population increased at a rate of 30% each month.**