nahannielsey
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The size of an exponentially growing bacteria colony doubles in 8 hours. How long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.

Verified Answer :

population ratio to original value is;
=2^(n/8) = 3

=ln[2^(n/8)]
= (n/8)ln(2)
= ln(3)
answer in exact and decimal form

n = 8ln(3)/ln(2)

n ~ 12.68
hope it helps

Answer:

12.68 hours

Step-by-step explanation:

The population growth function is,

\(y=ab^{x}\)

Where,

a = initial population,

b = growth factor per period,

x = number of periods

Here,

y = 2a, x = 8,

\(2a = a (b)^8\)

\(2=b^8\)

\(\implies b = 2^\frac{1}{8}\)

Thus, the function that shows the given situation would be,

\(y=a(2^\frac{1}{8})^x----(1)\)

If y = 3a,

\(3a=a(2^\frac{1}{8})^x\)

\(3=(2^\frac{1}{8})^x\)

\(\implies x = 12.68\)

Hence, after 12.68 hours the population would be tripled.

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