Question

The doubling period of a baterial population is 20 minutes. At time t = 120 minutes, the baterial population was 60000.

What was the initial population at time t = 0 ?

Find the size of the baterial population after 3 hours?

Answer 1

t = 0, initial population = 60 000 / (2 * 6) = 5 000

3 hours = 180 minutes. so if it doubles every 20 minutes, then it'll be
5 000 * 2 * 9 = 90 000

Answer 2

your equation for growth is

Pi*2^(t/20) where Pi is initial population and t is the time in minutes. t/20 is the number of 20 minute periods so you multiply by 2 that many times. We know after 120 minutes the pop is 60000. So we can solve for Pi

Pi*2^6=60000

Pi=(1875/2) or approximately 938

after 3 hours (180 minutes)

(1875/2)*2^(180/20)=1875/2*2^9=1875*2^8=480,000