Question

The population of bacteria in a petri dish doubles every 12 h. The population of the bacteria is
initially 500 organisms.
How long will it take for the population of the bacteria to reach 800?

1. thaiduong
Answer: 8.124 hours (rounding to 8 hours and 10 minutes)
Step-by-step explanation:
The logarithm function is used to simplify the complicated problems of multiplication and division. The time taken for the bacteria population to reach 800 is 8.124 h.
What is Logarithm?
The logarithm function is defined as the inverse of exponential function. If b = e^(a) then a is defined as a = log(b).
The logarithm of the product of two numbers is equal to the sum of their individual logarithms such as log(ab) = log(a) + log(b).
Given that,
The initial population of bacteria is N₀ = 500.
The time of doubling =  12 h
Then, after time t the the population of bacteria N can be written as,
N = N₀ × 2^(t / 12)
=> N =500 × 2^(t / 12)                                               (1)
Suppose, the time taken for the population to reach 800 be t.
In the form of equation it can be written as,
800 = 500 × 2^(t / 12)
=> 2^(t / 12) = 800 / 500
=> 2^(t / 12) = 1.6
Take logarithm both sides to get,
(t / 12) log(2) = log(1.6)
=> t / 12 = log(1.6) / log(2)
=>  t / 12 = 0.204 / 0.301
=>  t  = 0.677 × 12
=> t = 8.124
The time taken to reach bacteria population to 800 is 8.124 h.