# graph from logarithms

• Dec 4th 2008, 09:44 AM
bobchiba
graph from logarithms
http://img222.imageshack.us/img222/4545/offsz8.th.jpg

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?
• Dec 4th 2008, 10:48 AM
nzmathman
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.