Amarine biologist is studying the growth of a particular species of fish. she writes the following equation to show the length of the fish, f(m), in cm, after m months: f(m) = 5(1.07)m part a: when the marine biologist concluded her study, the length of the fish was approximately 9.19 cm. what 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 = 1 to m = 9, and what does it represent? (4 points)

the given growth  function for the length of the fish (cm) is

f(m) = 5(1.07)m = 5.35m

where 

m = months

at the end of the study, the length is 9.19 cm. the  time for conducting the study is determined as

5.35m = 9.19

m = 1.7178 months

part a.

the study was performed over a time period  of about 1.72 months. therefore  the domain for  plotting the function is 0 < = m < = 1.72.

note:

if growth  continues at this rate for up to m months, then the domain would be 0< =m< =m.

part b.

the growth function is a linear function.

when m=0, f=0.

therefore the initial growth is zero, which represents the y-intercept.

part c.

assume that the growth function is valid for 0< =m< =9.

the average rate of change of the function is the slope of the linear function, which is 5.35 cm/month.