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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.

Respuesta :

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,

[tex]y=ab^{x}[/tex]

Where,

a = initial population,

b = growth factor per period,

x = number of periods

Here,

y = 2a, x = 8,

[tex]2a = a (b)^8[/tex]

[tex]2=b^8[/tex]

[tex]\implies b = 2^\frac{1}{8}[/tex]

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

[tex]y=a(2^\frac{1}{8})^x----(1)[/tex]

If y = 3a,

[tex]3a=a(2^\frac{1}{8})^x[/tex]

[tex]3=(2^\frac{1}{8})^x[/tex]

[tex]\implies x = 12.68[/tex]

Hence, after 12.68 hours the population would be tripled.

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