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Answer:
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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