Question

a bacteria colony doubles in 7 hr. how long does it take the colony to triple? use N=N
02t/T where N0 is the initial number of bacteria and T is the time in hours it takes the colony to double. ( round to nearest hundredth as necessary)

Answer 1

\[2^{\frac{t}{7}}=3\] solve for \(t\)

Answer 2

but how

Answer 3

change of base formula gives \[\frac{t}{7}=\frac{\ln(3)}{\ln(2)}\] and so
\[t=\frac{7\ln(3)}{\ln(2)}\] and a calculator

Answer 4

11.09473751

Answer 5

is it right

Answer 6

i don't know, let me check

Answer 7

looks good to me
http://www.wolframalpha.com/input/?i=7log%283%29%2Flog%282%29

Answer 8

ok thanks you very much

Answer 9

A bit of explanation

[N / No] = (2)^(t/7)

ln [ ] = (t/7) ln(2)

t = 7 ln [ ] / ln(2)

ln [3] = 1.10
ln(2) =.693

t = 11.1