A colony of 200 bacterial cells is placed in a petri dish. After 5 hours, the bacteriologist finds 1,250 bacterial cells in the dish and assumes that the bacteria are growing at an exponential rate. In such a case, what is the growth constant associated with this colony of cells?

Use the general form of the exponential equation to represent the bacterial growth: $2635_w94_h20.png$, where Q is the population at time t, $5420_w20_h16.png$ is the initial population, and k is the growth constant.
Substitute the given values into the equation and solve for k:
$2718_w107_h17.png$, which gives
$8299_w83_h38.png$, and taking the natural log of both sides
$7982_w121_h38.png$, and isolating k
$6270_w139_h42.png$