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

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 2

12.68 hours

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^(1)/(8)`

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

`y=a(2^(1)/(8))^x----(1)`

If y = 3a,

`3a=a(2^(1)/(8))^x`

`3=(2^(1)/(8))^x`

`\implies x = 12.68`

Hence, after 12.68 hours the population would be tripled.