MATHEMATICS

it has been observed that a particular plant's growth is directly proportional to time. it measured 2 cm when arrived at the nursery and 2.5 cm exactly one week later. if the plant continues to grow at this rate, determine the function that represents the plants growthand graph it.

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  1. dh/dt = 2kt
    dh = 2kt dt
    h = kt^2 + C
    ...

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    oobleck
  2. growth in one week = .5 cm
    rate of growth in that week = .5/2 = .25

    f(t) = 2(1 + .25)^t, where t is in days
    f(t) = 2(1.25)^t

    check: when t = 1, f(1) = 2(1.25) = 2.5 cm
    after 4 weeks, f(4) = 2(1.25)^4 = 4.88 cm

    Of course t will have to have some logical upper value, and the rate of
    growth cannot continue like that.

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  3. exponential growth occurs when growth is proportional to the height ...

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    oobleck
  4. 2 cm , 2.5 cm
    well 2.5 cm = 2 cm * 1.25
    so every week multiply by 1.25
    2 , 2.5 ,
    2.5*1.25 ,
    2.5*1.25*1.25 ,
    2.5*1.25*1.25 , *1.25 ....
    that is a geometric sequence (Google math is fun geometric sequence)
    at week n, height = a r^k
    where a = 2.5 and r = 1.25
    height zero = a = 2.5
    height after 1 wk = a r^1 = 2.5 * 1.25
    etc

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  5. h = plant height

    h = 2 + .5t

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  6. I think they mean the growth dH/dt is proportional to time, not the height R_Scott , but indeed the wording is unclear.

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