The doubling period of a baterial population is 2020 minutes

The doubling period of a baterial population is  2020 minutes. At time t=80t80 minutes, the baterial population was 50000.

What was the initial population at time t=0t0?     

Find the size of the baterial population after 3 hours.

Solution

we use the formula

a(t)=a0* e^(kt)

where a(t) is the population at time t

and it doubles in 20 minutes

So if initiallt it is 1 then after 20 minutes it becomes 2

2=1 e^(20k)

taking ln on both sides

ln 2= 20k

k=ln2/20

50000=a0* e^(80ln2/20)

50000/ (e^80ln2/20)=a0

a0=3125

now we have to find the population after 3 hours and 3 hours=180minutes

a(180)= 3125×e^(180ln2/20)

= 1600000 approx