What was the initial population at time t=0? Find the size of the bacterial population after 3 hours.

Question

The doubling period of a bacterial population is  10 minutes. At time t=90 minutes, the bacterial population was 60000.

What was the initial population at time t=0?    

Find the size of the bacterial population after 3 hours. 

Answer 1

60,000 in 90 minutes

doubles every 10 minutes

30K at 80 min

15K at 70

7.5K at 60

3,750 at 50

1,875 at 40

937.5 at 30

468.75 at 20

234.375 at 10

117.1875 initially

A=Pe^rt

2=e^rt

2=e^10r

r=ln2/10= rate of change per minute

60,000=Pe^9ln2

P=60000/e^9ln2=117.1875

A=Pe^rt

=(6000/e^9ln2)e^18ln2=30,720,000 after 90 minutes

Answer 2

At t = 80 minutes the population was 60,000 / 2 = 30,000

At t = 70 minutes the population was 30,000 / 2 = 60,000 / 2² = 15,000

At t = 60 minutes the population was 15,000 / 2 = 60,000 / 2³ = 7,500

…

At t = 0 minutes the population was 60,000 / 2⁹ = 60,000 / 512 ≈ 117

On other hand 3 hours = 180 minutes

At t = 100 minutes the population was 60,000 x 2 = 120,000

At t = 110 minutes the population was 120,000 x 2 = 60,000 x 2² = 240,000

…

At t = 180 minutes the population was 60,000 x 2⁹ = 60,000 x 512 = 30,720,000