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.