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A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:

f(m) = 5(1.07)m

Part A: When the marine biologist concluded her study, the length of the fish was approximately 9.19 cm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)

Part C: What is the average rate of change of the function f(m) from m = 1 to m = 9, and what does it represent? (4 points)

Sagot :

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

: 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:

m = 0

=> f(0) = 5(1.07)⁰ = 5 cm

the length of the fish was approximately 9.19 cm.

=>

=>

=> 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

ghostadventures667

Step-by-step explanation:

The original function is f(m) = 5(1.07)^m, with the m as an exponent

part A) if the final length is 9.19, we can set f(m) = 9.19 and solve for m

plugging it into a calculator, I get m = ~8.99, so a bit less than 9. therefore, a reasonable domain might be all the m values 9 or below, or m ≤ 9

part B) the y-intercept of a function is the value of the independent variable when the dependent variable = 0. the two variables in your problem are height and number of months - which one do you think is the independent one, and which one is dependent? then re-interpret "value of the independent variable when the dependent variable = 0" in terms of the actual quantities that the variables represent

part C) average rate of change from m = 1 to m = 9

f(9)−f(1)9−1

evaluate, and think about what that represents in terms of height and number of months

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