I need a little help as to how to start this one.
At noon, the population of a bacterial culture was 2.4 x 10^6. At 4pm., the population was 6.2 x 10^7. Assume exponential growth. When will the population be 8.2 x 10^8?
Try the model $\displaystyle P=P_0e^{kt}$
With P = population and t = hours
you can say for $\displaystyle (t,P) = (0,2.4 \times 10^6) $
therefore $\displaystyle P_0 = 2.4 \times 10^6$
$\displaystyle P=2.4 \times 10^6\times e^{kt}$
Now use $\displaystyle (t,P) = (4,6.2 \times 10^7)$ to solve for k and you will have your model
After this $\displaystyle 8.2 \times 10^8$ goes into the model for P, solve for t.