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Math Help please!!! :)?

The number of students infected with flu at a school after t days is modeled by the function

p(t) = 600 / (1 + 19e^(-0.3t))

1. what was the initial number of students infected?

2. The school will close when 500 of the 600 students are infected. After how many days will it close?

Thanks in advance :)

2 Answers

Relevance
  • 9 years ago
    Favorite Answer

    For Question # 1 set 't' equal to zero and solve for p(t)

    hint: find p(0)

    For question # 2 find the time 't' when p(t) = 500

    so set p(t) = 500

    500 = 600 / (1 + 19e^(-0.3t))

    500 + 9500e^-0.3t = 600

    9500e^-0.3t = 100

    e^-0.3t = 100 / 9500

    take the natural log of both sides to get

    -0.3t = ln(100/9500)

    0.3t = - ln(100/9500)

    t = 15.18

    So after 15.18 days the school will close.

  • ?
    Lv 7
    9 years ago

    1) p(0) = 600/[1+19] = 30 students

    2) 500 = 600 / (1 + 19e^(-0.3t))

    1 + 19e^(-0.3t) = 600/500 = 1.2

    e^(-0.3t) = 0.2/19

    -0.3t = ln(0.2/19)

    t = 15.18 days

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