Describe the shape of the graph. What does the shape say about the relationship between mass and volume?
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Ответ:
Part A) A reasonable domain is the interval [0,8]
Part B) At the beginning of the study the length of the fish was 3 cm (see the explanation)
Part C) The average rate of change is 0.40\ cm/month (see the explanation)
Step-by-step explanation:
Let
m ---> the number of months
f(m) ---> the length of the fish in cm
we have
This is a exponential function of the form
where
a is the initial value or y-intercept
b is the base of the exponential function
b=1+r
r is the percent average of change
In this problem we have
Part A) When the marine biologist concluded her study, the length of the fish was approximately 5.98 cm. What is a reasonable domain to plot the growth function?
For f(m)=5.98 cm
substitute the given value in the function
solve for m
Apply log both sides
therefore
A reasonable domain is the interval [0,8]
Part B) What does the y-intercept of the graph of the function f(m) represent?
we know that
The y-intercept is the value of the function when the value of m is equal to zero
In this context the y intercept is the initial value of the function, or the starting size of the fish at month 0
For m=0
therefore
At the beginning of the study the length of the fish was 3 cm
Part C) What is the average rate of change of the function f(m) from m = 2 to m =2, and what does it represent?
we know that
To find the average rate of change, we divide the change in the output value by the change in the input value
the average rate of change is equal to
In this problem we have
Substitute
The average rate of change is how fast the growth changed over the time period