Calculus

After x weeks of prcatice, a student can type f(x)=80(1-e^-0.3x)words a minute. How sooon will the student be able to type 60 words per minute? (Round to the nearest tenth)

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  1. f(x)=80(1-e^-0.3x) = 60
    1-e^(-0.3x) = 60/80 = 3/4
    e^(-0.3x)=1-3/4=1/4
    e^(0.3x) = 4
    Take log to base e
    0.3x = ln(4)
    x = ln(4)/0.3 weeks.

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  2. You meant ln1/4

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  3. e^(-0.3x)=1-3/4=1/4
    =>
    -0.3x = ln(1/4)
    x=ln(1/4)/(-0.3)
    =ln(4)/0.3
    = approx. 4.6 weeks.

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