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
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
2*(t/16) = 1.6
t/16 log2 = log 1.6
t/16 = log1.6/log2 = 0.67807
t = 10.849
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.