To determine the domain of the function [tex]\( p(t) \)[/tex], which represents the rabbit population [tex]\( t \)[/tex] years from the start of Bethany's study, we need to understand what [tex]\( t \)[/tex] represents in this context.
1. Understanding the Variable [tex]\( t \)[/tex]:
- [tex]\( t \)[/tex] is the number of years from the start of the study.
- Since [tex]\( t \)[/tex] is measuring time from the start point, it cannot be negative.
2. Defining the Domain:
- The domain of a function includes all possible values that the independent variable (in this case, [tex]\( t \)[/tex]) can take.
- Since time cannot go backward, [tex]\( t \)[/tex] must be a non-negative number.
- Therefore, [tex]\( t \)[/tex] can take any value from 0 to positive infinity.
By considering these points, we conclude that the domain of [tex]\( p(t) \)[/tex] is all non-negative real numbers. Mathematically, this is represented as:
[tex]\[ [0, \infty) \][/tex]
Thus, the correct answer is:
B. [tex]\( [0, \infty) \)[/tex]
