Question

The number of bacteria present in a culture after t minutes is given as b=1000e^kt where k is a constant. If there are 8520 bacteria present after 15 minutes, find k and round to the nearest thousandth. a. 0.143 c. 2.143 b. 32.136 d. 0.13

Answer 1

To solve this problem, plug 8250 in for b and 15 in for t and then solve for k:

$8250=1000e^{15k}$

*Divide both sides by 1000*

$8.25=e^{15k}$

*Take the natural log (ln) of both sides*

2.1102=15k

*Divide both sides by 15*

0.1406=k

0.1406 rounds to 0.141 which is close to a. 0.143.

Hope this helps!!