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Question 201773: 6. The function f(x) gives the lake level over the passt year,with x measured in days and y, that is, the f(x) values, measured in inches above last year's mean height.
A. What it the real-world meaning of f(60)?
B. What is the real-world meaning of f(x)=-3?
C. What is an interpretation of f(x)=f(150?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x) = y, where:
x = number of days for which samples were taken this year.
y = the difference in the mean depth of the lake for the days that the sample was taken minus the mean depth of the lake for last year.
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an example:
last year the mean depth of the lake was 100 inches in depth.
this year a random sample was taken over 5 days.
this random sample showed the following:
sample 1: depth was 96 inches.
sample 2: depth was 100 inches.
sample 3: depth was 94 inches.
sample 4: depth was 90 inches.
sample 5: depth was 105 inches.
the mean of these random samples would be 485/5 = 97 inches.
the mean depth of the sample minus the mean depth of the lake for last year would be 97 - 100 = -3.
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f(5) = -3 would be the result of the calculation that showed this.
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from what I can tell, the function would not be an algebraic equation but some means of taking the sample data and then calculating the result from that.
the data might be supplied in a file that would then be read in by a program that summed the data, counted the number of samples taken, and then provided the result.
that program would also have to read in the data from last year and calculate that, or read in the results from last year and use it to determine the difference in the means.
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To be more specific in answering your question,
A). f(60) means that x = 60 means that the number of days that samples were taken was 60.
B). f(x) = -3 means that from a sample of x days, the mean depth of the lake was 3 inches less than the mean depth of the lake last year. Note that where you say height I say depth but we are talking about the same thing.
C). f(x) = f(150) doesn't ring any bells for me. Not sure what they are talking about. f(150) means a 150 days of samples we taken. the result would be some measurement in inches above or below the mean of last year. if f(150) was equal to some number, this would mean that f(x) = that number.
example:
f(150) = 15
f(x) = f(150)
this would mean that f(x) = 15.
other than that, this last statement would have no meaning for me. I can't see where it would apply.
It could also mean that they want a sample of 150.
Why anybody would even write it this way is unknown to me.
Answer by ikleyn(52957)  (Show Source):
You can put this solution on YOUR website! .
The function f(x) gives the lake level over the passt year, with x measured in days and y, that is, the f(x) values, measured in inches above last year's mean height.
A. What it the real-world meaning of f(60) ?
B. What is the real-world meaning of f(x)=-3 ?
C. What is an interpretation of f(x)=f(150) ?
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Tutor @Theo in his post produced very long answers, which I even can not read (so wordy they are).
It is difficult to me to believe (~ to imagine) that somebody in the world will read so long writing.
In that follows I will give my short answers.
A. f(60) is the level in the lake on the 60-th day;
or, in more precise terms, f(60) tells us that on the 60-th day the water level in the lake
was f(60) inches above or below the last year average water level
(depending on the sign of f(60): if f(60) >= 0, then above,
and if f(60) < 0, then below).
B. f(x) = -3 means that on the day 'x' the water level in the lake was 3 inches below the last year average level.
C. f(x) = f(150) means that the water level in the lake on day 'x' was the same as that of the 150-th day.
Solved: all questions are answered.
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