1.1. An exponential growth model for the number of bacteria in an experiment is of the form

$N={N}_{0}{a}^{kt}$

$N$ is the number of bacteria and $t$ is the time in hours since the experiment began. ${N}_{0},a$ and $k$  are constants.

A scientist records the number of bacteria at various points over a six-hour period. The results are in the table below.

By plotting ${log}_{2}N$ against $t$, drawing a line of best fit and finding its equation, estimate the values of ${N}_{0}$,$a$ , and $k$.

1.2. What does the model predict for the value of $N$ after twelve hours? Comment on the reliability of this prediction.