The percentage of obese children aged 12-19 years in the United States is approximately P(t) = 0.04t + 4.6 if 0 ≤ t < 10 −0.01005t2 + 0.9

Question

The percentage of obese children aged 12-19 years in the United States is approximately P(t) = 0.04t + 4.6 if 0 ≤ t < 10 −0.01005t2 + 0.945t − 3.4 if 10 ≤ t ≤ 30 where t is measured in years, with t = 0 corresponding to the beginning of 1970. What was the percentage of obese children aged 12-19 at the beginning of 1975? At the beginning of 1985? At the beginning of 1990?† (Round your answers to two decimal places.) 1975 % 1985 % 1990 %

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Gia Bảo 5 years 2021-07-24T09:21:06+00:00 1 Answers 124 views 0

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  1. Philomena
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    2021-07-24T09:22:52+00:00
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    Answer:

    1975—— 4.8%

    1990 —— 11.48%

    1985 —— 8.51%

    Step-by-step explanation:

    Given

    P(t) = 0.04t + 4.6 if 0 ≤ t < 10

    P(t) = -0.01005t^2 + 0.945t - 3.4 if 10 ≤ t ≤ 30

    Where

    t:=0 implies year = 1970

    Solving (a): Beginning of 1975.

    First, we calculate the value of t

    t = 1975 - 1970

    t = 5

    This falls in the range: 0 ≤ t < 10

    So:

    P(t) = 0.04t + 4.6

    P(5) = 0.04 * 5 + 4.6

    P(5) = 4.80

    Solving (b): Beginning of 1990.

    t = 1990 - 1970

    t = 20

    This falls in the range: 10 ≤ t ≤ 30

    So:

    P(t) = -0.01005t^2 + 0.945t - 3.4

    P(20) = -0.01005*20^2 + 0.945*20 - 3.4

    P(20) = 11.48

    Solving (c): Beginning of 1985

    t = 1985 - 1970

    t = 15

    This falls in the range: 10 ≤ t ≤ 30

    So:

    P(t) = -0.01005t^2 + 0.945t - 3.4

    P(15) = -0.01005*15^2 + 0.945*15 - 3.4

    P(15) = 8.51375

    P(15) = 8.51

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