Question

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.

Answer 1

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.

Answer 2

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