The size of an exponentially growing bacteria colony doubles in 5 hours.?
How long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.
Decimal (nearest hundreth):
- FazLv 71 decade agoFavorite Answer
Find the growth rate:
2 = e^(5r)
r = ln2 / 5
To triple therefore, solve the following for t:
3 = e^((ln2/5)t)
t = 5ln(3) / ln(2) (exact)
t = 7.92 hours (approx)
- railbuffLv 71 decade ago
PN = PS(2^(t/5)) where PS is the population at start and PN is the population after t hours. Evaluate t, for PN = 3(PS)
3(PS) = PS(2^(t/5))
3 = 2^(t/5)
log3 = log[2^(t/5)]
log 3 = (t/5)log2
(log3)/log2) = t/5
5(log3)/(log2) = t
There are no exact values for logs - most are irrational numbers.
log(3) = 0.477121254...
log(2) = 0.3010249995...
t = 5(0.477121254...)/(0.3010249995...)
= 7.92 hours to the nearest hundredthSource(s): Retired math teacher