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Ryan
Ryan asked in Science & MathematicsMathematics · 5 years ago

Calculus question using e?

height of a tree =

h(t) = (140)/(1+210e^-0.24t)

t is the age of the tree in years

estimate the age of a 70 foot tree

3 Answers

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  • DWRead
    Lv 7
    5 years ago

    You are missing a set of parentheses.

    h(t) = 140/(1+210e^(-0.24t))

    70 = 140/(1+210e^(-0.24t))

    1+210e^(-0.24t) = 140/70 = 2

    210e^(-0.24t) = 1

    e^(-0.24t) = 1/210

    -0.24t = ln(1/210)

    t = ln(1/210)/(-0.24) ≅ 22.3 years

  • cidyah
    Lv 7
    5 years ago

    h(t) = (140)/(1+210e^-0.24t)

    70 = 140 / (1+ 210 e^(-0.24t) )

    70 ( 1+ 210 e^(-0.24t) ) = 140

    70 + (210)(70) e^(-0.24t) = 140

    (210)(70) e^(-0.24t) = 140-70

    14700 e^(-0.24t) = 70

    e^(-0.24t) = 70/14700

    -0.24t = ln (70/14700)

    t = - ln(70/14700) / 0.24

    t = 22.28 years (age of tree)

  • Bryce
    Lv 7
    5 years ago

    70=140/[1+210e^(-0.24t)]

    1+210e^(-0.24t)=2

    e^(-0.24t)=1/210

    -0.24t=ln(1/210)

    t≈22.3 years old

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