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
