Abel says (6^2)^3 = 6^5. Is he correct? Explain.

Answer :

Nope !

Using PEMDAS you can solve this step by step :

  1st solve what's in the parentheses "( 6^2)" :

6 × 6 = 36

  Then solve "36^3" :

36 × 36 × 36 = 46,656

  Next solve the other equation "6^5" :

6 × 6 × 6 × 6 × 6 = 7,776

So, ( 6^2 )^3 ≠ 6^5

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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.