150 bacteria grow continuously, tripling every 2 hours. How many hours will it take for the bacteria count to reach 200,000?

Question

What's the initial equation?

What's the equation in logarithmic form?

Solution:

Answer 1

3 = e^2r

ln3 = 2r

r = (ln3)/2= about .5493

200,000 = 150e^tln3

200,000/150 = e^rln3

20,000/15 = e^tln3

4,000/3 = e^tln3

1.333 1/3 = e^.5493t

ln(1,333.333..) = .5493t

t = ln(1,333.333...)/.5493

t = about 13.1 years

rough check on the answer:

triples every 2 years

150 in year 0

450 year 2

1350 year 4

4050 year 6

12,150 in 8

36,450 in 10

109,350 in 12 years

328,050 in 14 years

200,000 between 12 and 14 years

12<t<14

t = 13.1