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Thread: graph from logarithms

  1. #1
    Mar 2007

    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
    Dec 2008
    Auckland, New Zealand
    Make a table with values for $\displaystyle \ln(N)$.

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

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

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

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

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

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