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?
Round your answer to the nearest tenth of an hour.
500 (2^(t/12)) = 800 , where t is in hours
2^(t/12) = 1.6
take logs of both sides, and use the rules of logs
t/12 log2 = log 1.6
t/12 = log 1.6/log 2
t = 12(log 1.6/log 2)
= appr 8.1 hours
t=8.136864
-nutz
To find the time it takes for the population of the bacteria to reach 800, we can use the formula for exponential growth:
N = N0 * 2^(t/h)
Where:
N = final population
N0 = initial population
t = time elapsed
h = doubling time
Plugging in the given values:
800 = 500 * 2^(t/12)
To solve for t, we need to isolate the exponent. Divide both sides of the equation by 500:
800/500 = 2^(t/12)
Divide both sides by 2 to isolate the exponent:
1.6 = 2^(t/12)
Take the logarithm (base 2) of both sides to solve for t:
log2(1.6) = t/12
Using a calculator, we find that log2(1.6) ≈ 0.737
Multiply both sides by 12 to solve for t:
0.737 * 12 = t
t ≈ 8.84
Therefore, it will take approximately 8.8 hours for the population of bacteria to reach 800.
To find out how long it will take for the population of bacteria to reach 800, we need to use the given information that the population doubles every 12 hours and the initial population is 500 organisms.
Let's set up an equation to solve for the time it takes for the population to reach 800.
Let t represent the time in hours.
After t hours, the population of bacteria will be 500 * 2^(t/12) organisms.
We want to solve for t when the population reaches 800, so we can set up the following equation:
500 * 2^(t/12) = 800
Now, we can solve this equation to find the value of t.
Divide both sides of the equation by 500:
2^(t/12) = 800/500
Simplify:
2^(t/12) = 8/5
Take the logarithm of both sides of the equation (using base 2 since we have a power of 2):
log2(2^(t/12)) = log2(8/5)
Using the property of logarithms, we can bring down the exponent:
(t/12) * log2(2) = log2(8/5)
Simplifying:
(t/12) = log2(8/5)
Now, we can solve for t:
t = 12 * log2(8/5)
Using a calculator or logarithmic table, we can determine that log2(8/5) is approximately 0.678.
Substituting this value back into the equation:
t ≈ 12 * 0.678
t ≈ 8.136
Rounding to the nearest tenth of an hour, it will take approximately 8.1 hours for the population of bacteria to reach 800.