What is the answer?

Question

The count in a bacteria culture was 100 after 20 minutes and 1300 after 35 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?    

Find the doubling period.    

Find the population after 115 minutes.    

When will the population reach 14000.   

Answer 1

100=Poe^20r

1300=Poe^35r

13=e^15r

ln13=15r

r=ln13/15=.171 = 17.1% growth rate per minute

100=Poe^3.42

Po=100/e^3.42=about 3.2712435=initial population

2=e^.171t

t=ln2/.171=4.0535 minutes = doubling time

P=3.27e^115(.171)= 1.13487686x10^9=1,134,876,860= about 1.1 billion after 115 minutes

14000=3.27e^.171t

t= ln(14000/3.27)/.171= about 48.9 minutes to reach 14,000

doubling time = about 4 minutes

100 in 20

roughly

200 in 24

400 in 28

800 in 32

1300 in 35

1600in 36

3200 in 40

6400 in 44

12800 in 48

14000 in 49.9