1. ## 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?

2. 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.