Final answer:
The student's question is about applying mathematical concepts such as the domain of a function, understanding the y-intercept, and calculating the average rate of change in the context of marine biology to study fish growth.
Step-by-step explanation:
The question relates to the application of mathematical concepts in biology, specifically in the study of fish growth by a marine biologist. To answer this question, consider the following:
- a) Reasonable domain to plot the growth function: The domain for plotting the growth function of a species of fish would typically start at m = 0, representing the fish at birth (or hatching), and extend to the maximum age the fish could live in their natural environment or under the study's conditions.
- b) Y-intercept of the graph: The y-intercept of the growth function f(m) represents the size of the fish at birth (or hatching), assuming that the function represents size as a function of age (m).
- c) Average rate of change: The average rate of change of the function f(m) from m = 2 to m = 8 is calculated as [f(8) - f(2)]/(8 - 2). This represents the average growth rate of the fish between the ages of 2 and 8.
These mathematical concepts can help the marine biologist understand and predict the growth of the fish species being studied.