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.