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# 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.

Exact:

Decimal (nearest hundreth):

### 3 Answers

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- 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...)

= 7.924812504....

= 7.92 hours to the nearest hundredth

Source(s): Retired math teacher

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