Final answer:
The best domain for the function w(t) = 5(1.2)^t, given the context of the groundhog's growth from 5 oz to about 80 oz, is (0,15]. It represents the time in months from the beginning of the study to when it concluded.
Step-by-step explanation:
The question is asking to choose the most suitable domain for the function w(t) = 5(1.2)^t, which represents the weight of a groundhog over time. To find this, we must consider the context in which the weight changes from 5 oz to about 80 oz. Since the weight at t=0 is given as 5 oz, the domain must include the starting point t=0. As the study concluded when the groundhog was about 80 oz, we need to determine the value of t when the weight achieves this approximate value. It is important to note that the domain represents the time in months, so it should not include negative values or values beyond which the study was completed.
The best domain in this context would be the interval that starts from 0 and goes up to the time it takes the groundhog to reach approximately 80 oz, excluding the time after the study ended. Since the weight must reach or exceed 80 oz for the study to conclude and we're considering months as our unit of time, based on the growth model, the option (0,15] includes the entire growth period up to when the weight reaches 80 oz, thus answering the student's homework question.