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Math Help - graph from logarithms

  1. #1
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    Joined
    Mar 2007
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    80

    graph from logarithms



    For the above questions, I have done question a) but im not sure how to go about question b). I don't have a problem creating the graph but am unsure as to making a new table of values?

    Any thoughts?
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  2. #2
    Member
    Joined
    Dec 2008
    From
    Auckland, New Zealand
    Posts
    189
    Make a table with values for \ln(N).

    Plot a graph of t \quad vs. \quad \ln(N), which should give you a relatively straight line, as they have told you the data can be modeled by an exponential function.

    Because if
    N = N_0 e^{kt} \,,

    \ln(N) = \ln(N_0 e^{kt})

    \ln(N) = \ln(N_0) + \ln(e^{kt})

    \ln(N) = A + kt
    letting ln( N_0) = A

    Your graph has y = \ln(N) and x = t.
    This equation is in the form y = mx + c, thus the graph is a straight line and thus verifies that the data follows the exponential relationship.
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