Math

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Can you help me set up this problem please

P(t) = 100/1+48.2e^-0.52t

If the company's claim is true, how many months will it take to have mastered 80% of the program.

I just need help setting it up

Thanks!

  • Math -

    I will assume you meant

    P(t) = 100/(1+48.2e^(-.52t) )

    You did not define P(t), but I will assume it will be the
    "efficiency" mastered after t months
    so .....

    .8 = 100/(1 + 48.2e^(.52t))
    .8 + 38.56e^(.52t) = 100
    e^(.52t) = (100-.8)/38.56 = 2.572614
    taking ln of both sides, and knowing that ln e = 1
    .52t = ln (2.572614)
    t = 1.817 or appr 1.8 months

    check:
    let t=1.817
    P(1.1817) = 100/(1 + 48.2e^(.52(1.817)
    = 0.8

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