Shaun drew δlmn, in which m∠lmn = 90°. he then drew δpqr, which was a dilation of δlmn by a scale factor of 3 from the center of dilation at point m. which of these can be used to prove δlmn ~ δpqr by the aa similarity postulate?
segment lm = 3segment pq; this can be confirmed translating point p to point l.
segment mn = 3segment qr; this can be confirmed translating point r to point n.
m∠p ≅ m∠n; this can be confirmed by translating point p to point n.
m∠r ≅ m∠n; this can be confirmed by translating point r to point n.

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.