When solving for k round to four decimal places A culture st

When solving for k. round to four decimal places. A culture started with 6,000 bacteria. After 3 hours, it grew to 7,200 bacteria. Predict how many bacteria will be present after 19 hours. Round your answer to the nearest whole number.

Solution

P = Ae^kt . After 3 hours, 6000 bacteria increase to 7200. Therefore, we have 7200 = 6000e^3k or, e^3k = 7200/6000 = 6/5 = 1.2. Taking natural logarithms of both the sides, we have 3k lne = ln 1.2 or 3k = 0.18232 or, k = 0.0608 [ as ln( e)= 1]. Then, after 19 hours, the number of bacteria will be 6000e19k = 6000e^19*0.0608 = 6000e^1.1547 = 6000e^1.1547 = 6000* 3.17307135 = 19038.43 = 19038 ( on rounding off to the nearest whole number).