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Lucid7930
20.09.2021 •
Mathematics
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Ответ:
Part A) A reasonable domain is the interval [0,10]![0\leq n\leq 10](/tpl/images/0454/5406/7ff10.png)
Part B) The y-intercept is the height of the plant at the begin of the scientist study (initial height of the plant)
Part C) The average rate of change is
(see the explanation)
Step-by-step explanation:
Part A) When the scientist concluded his study, the height of the plant was approximately 16.13 cm. What is a reasonable domain to plot the growth function?
we have
where
n is the number of days
f(n) is the height of the plant in cm
For f(n)=16.13 cm
substitute
solve for n
Apply log both sides
therefore
A reasonable domain is the interval [0,10]
Part B) What does the y-intercept of the graph of the function f(n) represent?
we have
The y-intercept is the value of y when the value of x is equal to zero
In this context the y-intercept is the height of the plant at the begin of the scientist study (initial height of the plant)
For n=0
Part C) What is the average rate of change of the function f(n) from n = 3 to n = 10, 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
In this problem we have
Substitute
it tells us that the plant on average grows 0.43 cm each day, between day 3 and day 10