The count in a bacteria culture was 800 after 15 minutes

Question

The count in a bacteria culture was 800 after 15 minutes and 1700 after 30 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?   

Find the doubling period.   

Find the population after 70 minutes.   

When will the population reach 13000. 

Answer 1

800 = Ab^15

1700 = Ab^30

A = 800/b^15 = 1700/b^30

b^30/b^15 = b^15 = 1700/800 = 17/8 = 2.125

b = 15th root of 2.125 = about 1.05

A = 800/(17/8) = 6400/17 = 376.47 = initial amount

doubling time: 2A = A(1.05)^t

(1.05)^t = 2

t = 14.21 minutes (in 15 minutes it slightly more than doubled, 800 to 1700, so doubling time is a little less than 15 minutes)

P = 376.47(1.05)^70 = 11454.64 after 70 minutes

13,000 = 376.47(1.05)^t

(1.05)^t = 13,000/376.47 = 34.53

t =72.60 minutes

Answer 2

Answered above.