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 wa

Question

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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Khánh Gia 4 years 2021-08-14T18:25:30+00:00 1 Answers 44 views 0

Answers ( )

  1. thanhcong
    0
    2021-08-14T18:27:07+00:00
    Reply

    Answer:

    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

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