A colony of bacteria is growing exponentially, doubling in size every 140 minutes. How many minutes will it take for the colony of bacteria to become five times its current size?

Question

amistre64 · Answer

need to define the rate

amistre64 · Answer

ln(2)/t = r  just as a notion

amistre64 · Answer

A = Pe^rt

2P = Pe^rt

2 = e^rt

ln(2) = rt

ln(2)/t = r

....................

A = Pe^(ln(2)/t) t'

A = Pe^(ln(2)/t) t'

5P = Pe^(ln(2)/t) t'

5 = e^(ln(2)/t) t'

ln(5) = (ln(2)/t) t'

ln(5)/(ln(2)/t) =  t'

maybe  depending on what they current size might be?

amistre64 · Answer

$$t'=log_2(5^{140})$$
is my guess

amistre64 · Answer

325.07 minutes ... IF im right lol

anonymous · Answer

yes you're right. I just wanted to check my answer. Thank you!!

amistre64 · Answer

yep