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 1,000 bacteria. After 2 hours, it grew to 1,200 bacteria. Predict how many bacteria will be present after 13 hours. Round your answer to the nearest whole number. P = Ae^kr

Solution

P = Ae^kt After 2 hours, 1000 bacteria grow to 1200 bacteria. Therefore, 1200 = 1000e^3k or, e^3k = 1200/1000 = 1.2. On taking natural logarithms of both the sides, we have 3k(ln e ) or, 3k = ln 1.2 ( as ln e = 1) or k = 1/3 (ln 1.2) = ( 1/3) (0.182321556) = 0.0608.

After 13 hours, the number of bacteria will be 1000e^{13* 0.0608} = 1000e^0.79006  =  1000* 2.20352863401 = 2203.528634 = 2204 ( on rounding off to the nearest whole number)