nicki76
03.10.2020 •
Mathematics
A student records the height of the water in a pool each day for seven days. The function h(t) = |t-3|+14
models the height of the water h (in feet) in the pool after t days. Find the domain and range for this function and
interpret their meaning in the context of the problem.
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Ответ:
When we have a function like h(t)
The domain is the set of the possible values of t.
In this case, we know that the measure lasts for 7 consecutive days, so t represents the number of days.
Then the possible values of t are:
t ∈ {1, 2, 3, 4, 5, 6, 7}
Now, let's look at the range.
The range is the set of the possible values that h(t) can take.
Then:
h(1) = I1 - 3I + 14 = 16
h(2) = I2 - 3I +14 = 15
h(3) = I3 - 3I + 14 = 14
h(4) = I4 - 3I + 14 = 15
h(5) = I5 - 3I + 14 = 16
h(6) = I6 - 3I + 14 = 17
h(7) = I7 - 3I + 14 = 18.
Then the possible values of the range are:
R = {14, 15, 16, 17, 18}
This is when we only let t to be natural numbers, if we allow t to be a real number, we will have all the values in between the natural numbers written above, then the domain is:
D: 1 ≤ t ≤ 7
And the range is:
R: 14ft ≤ h(t) ≤ 18ft
Ответ: