Question

A marine biologist is studying the growth of a particular species of fishShe writes the following equation to show the length of the fish f(m) in after m months f(m) = 3 * (1.09) ^ m Part A: When the marine biologist concluded her study, the length of the fish was approximately 5.98 cmWhat is a reasonable domain to plot the growth function? (4 points) Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points) Part C: What is the average rate of change of the function f(m) from m = 2 tom m = 8 and what does it represent? (4 points)

Answer 1

Answer:

The given equation is:

f(m) = 3(1.09)^m

where 'f(m)' represents the length of the fish after 'm' months.

Domain is considered as a set of all values of input. In this question, the input is number of months. The input should starts at 0 which will show the initial height and then as the number 'm' increases, the value of f(m) also increases.

Thus, the domain can be defined as m ≥ 0

y-intercept occurs at m=0. It means the height of the fish after 0 months, which can also be considered as initial height.

Calculate the value of function for m=2 and m=8

For m=2, f(2) = 3.564

For m=8, f(8) = 5.978

Average rate of change = (5.978-3.564) / (8-2)

Average rate of change = 0.402

It means the fish grows about 0.402cm each month in between 2 to 8 months