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Thread: Another problem

  1. #1
    Newbie AknightwhosayNi's Avatar
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    Another problem

    Here's the last of the problems that i'm not sure how to tackle.
    A group of students where studying how fast a plant was growing. Once a day they measured the plant. These was the results:
    Day--- length (cm)
    0 -----0,5
    1 -----0,8
    2 -----1,3
    3 -----2,1
    4 -----3,3
    5 -----5,2
    6 -----8,1
    7 -----13,4

    The students created an equation from this information: y=0,5*1,6^X
    X is time in days. Y is the height of the plant.
    How did the students work out 1,6 from this information?
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  2. #2
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    Hello, AknightwhosayNi!


    A group of students where studying how fast a plant was growing.
    Once a day they measured the plant. These are the results:

    . . $\displaystyle \begin{array}{c|c}
    \text{Day} & \text{Height} \\ \hline
    0 & 0.5 \\ 1 & 0.8 \\ 2 & 1.3 \\ 3 & 2.1 \\ 4 & 3.3 \\ 5 & 5.2 \\ 6 & 8.1 \\ 7 & 13.4 \end{array}$

    The students created an equation from this information: .$\displaystyle y\:=\:0.5\cdot 1.6^x$
    . . where $\displaystyle x$ is time in days, $\displaystyle y$ is the height of the plant in cm.

    How did the students work out 1.6 from this information?

    They conjectured that the function is of the form: .$\displaystyle y \;=\;A\cdot B^x$

    To determine $\displaystyle A$ and $\displaystyle B$, use two values from the table.
    . . We'll use the first two values . . .

    $\displaystyle x=0,\;y=0.5\!:\quad 0.5 \:=\:A\cdot B^0 \quad\Rightarrow\quad A \:=\:0.5$

    . . Hence, the function (so far) is: .$\displaystyle y \;=\;0.5\cdot B^x$


    $\displaystyle x = 1,\;y = 0.8\!:\quad 0.8 \:=\:0.5B^1 \quad\Rightarrow\quad B \:=\:\frac{0.8}{0.5} \:=\:1.6$


    Therefore, the function is: .$\displaystyle y \;=\;0.5\cdot1.6^x$

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  3. #3
    Newbie AknightwhosayNi's Avatar
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    I see... Thanks!
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