The population of a bacteria in a Petri dish doubles every 16 hours. The population of the bacteria is initially 500 organisms.
How long will it take for the population of the bacteria to reach 800?
Round your answer to the nearest tenth of an hour.
8.7 h
10.8 h
11.1 h
12.6 h <my choice
500*2^(t/16) = 800
2*(t/16) = 1.6
t/16 log2 = log 1.6
t/16 = log1.6/log2 = 0.67807
t = 10.849
10.8 Trust me, just got my test results
In a lab experiment, 70 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 5 hours. How many bacteria would there be after 29 hours, to the nearest whole number?
To determine how long it will take for the population of the bacteria to reach 800, you can use the formula for exponential growth:
P(t) = P(0) * 2^(t/h)
Where:
P(t) is the population at time t
P(0) is the initial population
t is the time in hours
h is the doubling time in hours
In this case, the initial population is 500 bacteria, and the doubling time is 16 hours. Now, we need to solve for t when P(t) = 800:
800 = 500 * 2^(t/16)
Divide both sides of the equation by 500 to isolate the exponential term:
(800/500) = 2^(t/16)
Simplify the left side:
1.6 = 2^(t/16)
Now, take the logarithm of both sides of the equation to solve for t:
log(1.6) = log(2^(t/16))
Using the logarithmic property, we can bring down the exponent:
log(1.6) = (t/16) * log(2)
Solve for t by multiplying both sides of the equation by 16 and dividing by log(2):
t = (16 * log(1.6)) / log(2)
Using a calculator, you can find log(1.6) and log(2). After plugging in the values and calculating the equation, you will find that:
t ≈ 10.8 h
So, it will take approximately 10.8 hours for the population of bacteria to reach 800 organisms.