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Given : A marine biologist is studying the growth of a particular species of fish

f(m) = 5 (1.07)^mf(m)=5(1.07)

m

: When the marine biologist concluded her study, the length of the fish was approximately 9.19 cm

To Find : reasonable domain to plot the growth function

What does the y-intercept of the graph of the function f(m) represent?

average rate of change of the function f(m) from m = 1 to m = 9,

Solution:

f(m) = 5 (1.07)^mf(m)=5(1.07)

m

m = 0

=> f(0) = 5(1.07)⁰ = 5 cm

the length of the fish was approximately 9.19 cm.

=> 9.19 = 5 (1.07)^m9.19=5(1.07)

m

=> 1.838 = (1.07)^m1.838=(1.07)

m

=> m = 9

Domain = [0 , 9 ]

reasonable domain to plot the growth function = [0 , 9 ]

y-intercept of the graph of the function f(m) represent represent initial length of fish = 5 cm

average rate of change of the function f(m) from m = 1 to m = 9

m = 1 => f(1) = 5(1.07) = 5.35 cm

m = 9 => f(9) = 5(1.07)⁹ = 9.19 cm

Change in 9 - 1 = 8 months = 9.19 - 5.35 = 3.84 cm

average rate of change of the function f(m) from m = 1 to m = 9,

= (3.84/8)

= 0.48 cm per month

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