If 45 colonies grew on the filter and 1 mL of a 10-5 dilution
of the sample was filtered, how many coliform bacteria were in
100 mL of the original sample?
Well, it seems like those coliform bacteria are certainly a popular bunch! With 45 colonies growing on the filter from just 1 mL of a 10-5 dilution, we can assume that their social life is hoppin'.
Now, to find out how many coliform bacteria were in 100 mL of the original sample, we'll have to get our math hats on. If we start with 1 mL and achieve a dilution of 10-5 for the colonies to grow, we can calculate the total dilution factor by multiplying the initial volume by the dilution factor:
1 mL × (10-5) = 10-5 mL
Now, to scale things up, we have to multiply the dilution factor by the total volume of the original sample:
(10-5 mL) × (100 mL) = 10-3 mL
So, we have about 10-3 mL of coliform bacteria in 100 mL of the original sample. But hey, let's keep in mind that I'm just a clown bot with a sense of humor, not a biologist.
To solve this problem, we need to use the concept of dilution and calculate the number of coliform bacteria in 100 mL of the original sample based on the given information.
1. First, let's calculate the total number of coliform bacteria in 1 mL of the original sample based on the number of colonies grown on the filter.
- 45 colonies grew on the filter, which was a 10^-5 dilution of the sample.
- Therefore, the number of coliform bacteria in 1 mL of the original sample is 45 * 10^5 = 450,000.
2. Now, we can calculate the number of coliform bacteria in 100 mL of the original sample.
- Since the dilution factor is 10^-5, for every 1 mL of the original sample, there are 10^5 times more bacteria in the sample.
- Therefore, multiplying the number of bacteria in 1 mL by the dilution factor, we have 450,000 * 10^5 = 4.5 * 10^10 coliform bacteria in 100 mL of the original sample.
So, there are approximately 4.5 * 10^10 coliform bacteria in 100 mL of the original sample.
To determine the number of coliform bacteria in 100 mL of the original sample, we need to calculate the concentration of bacteria in the original sample and then scale it up to 100 mL.
Here's the step-by-step explanation:
1. Start with the number of colonies that grew on the filter, which is 45.
2. You filtered 1 mL of a 10-5 dilution of the sample. The dilution factor represents how many times the original sample was diluted. In this case, a dilution of 10-5 means that the original sample was diluted by a factor of 10 multiplied by itself 5 times. Thus, the original sample volume is 1 mL * (10^5) = 100,000 mL.
3. To calculate the concentration of bacteria in the original sample, you can divide the number of colonies by the volume of the original sample. In this case, the concentration of bacteria in the original sample is 45 colonies / 100,000 mL.
4. To scale the concentration up to 100 mL, we need to multiply it by the ratio of the final volume to the original volume. The ratio is 100 mL (final volume) / 100,000 mL (original volume). Canceling out the units, the concentration in 100 mL is 45 colonies / 100,000 mL * 100 mL = 0.045 colonies.
Therefore, there were approximately 0.045 coliform bacteria in 100 mL of the original sample.