A bacteria culture initially contains 2000 bacteria and doub

A bacteria culture initially contains 2000 bacteria and doubles every half hour. Find the size of the bacterial population after 20 minutes and after 7 hours.

Solution

N= Noe^(kt)

find k using the informtaion: bacteria culture initially contains 2000 bacteria and doubles every half hour

2No = Noe^(0.5k)

ln2 = 0.5k ----> k= 1.386

intial amount : No = 2000

N = 2000e^(1,386t)

after 20min = 0.33 hr

N = 2000e^(0.33*1.386) = 2000*1.58 = 3160 bacterias

after 7hrs : N = 2000e^(1.386*7) = 2000*16350.275 = 32700550.14 =32700550 bacterias