Generation Times - Video Tutorials & Practice Problems

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Generation Times

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in this video, we're going to begin our lesson on generation times. And so scientists can actually measure the growth rate of a microbial population by calculating its generation time. Now the generation time is also sometimes referred to as the doubling time and that's because this is the amount of time it takes for a population to double and the number of cells. And in other words, the generation time or the doubling time represents how long it takes for binary vision to occur. And for binary fission to make a new generation of cells. And recall from our previous lesson videos that binary vision is the name of the process by which pro carry attic cells divide. And so the generation time is just how long binary fission takes. And so different microbes are going to 10 or tend to have different generation times. And so some microbes will divide really, really, really slow, whereas other microbes will divide really, really fast. And so if we take a look at our image down below, we can get a better understanding of the different generation times. And so over here on the left, notice that we're showing you a microbe that divides really, really slow. Like this turtle that we have over here which we know turtles move really slow And so you can see that over a period of 30 minutes. Uh this pro carry attic cell is able to divide into two cells. And so the generation time for this microbe is 30 minutes. Whereas if we take a look at the right side of the image, notice we're showing you a microbe that divides really, really fast like this bunny rabbit that you see over here. And so notice that in half the time in just 15 minutes this microbe is able to divide to create a new generation of cells and over a period of 30 minutes uh these cells are able to divide once again, and so this microbe over here is going to have a much faster generation time. And so you can see that shorter times represent faster uh binary fission, whereas longer times represent longer binary fission processes. And so this year concludes our brief introduction to generation times. And later in our next video, we'll talk about how scientists can use these generation times to predict how many cells there will be after a given amount of time. So I'll see you all in that next video to talk about that.

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Calculating Generation Times

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5m

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in this video, we're going to talk about using generation times to calculate the number of cells. And so if you are given the generation time for a particular microbial population, then the following equation, which you can see down below right here can be used to calculate the number of cells after a certain period of time. And so notice that in this equation there are several different variables that we define down below. And so the first of these variables is N. T. And n. T. Is equal to the final number of cells after a given amount of time. Then we have N not or N here and and not as equal to the initial number of cells at the very beginning. And this is going to be multiplied by two, raised to the power of N where N is an exponent here and N is equal to the number of new generations over a given amount of time. And you can get in by taking the given amount of time and dividing it by the generation time which should be given to you. And so to show you how this equation here can be applied, we have an example down below And notice that this example here says to calculate the number of cells after three hours of growth, starting from 10 cells with a generation time of minutes. And so once again we want to use this equation that's up above. So we'll start with the very first variable here, N. T. And N. T. Once again is the final number of cells after a given amount of time. And notice that this is really what we want to calculate. We want to calculate the final number of cells after three hours of growth. And so N. T. Is our missing variable that we need to solve for. So we can go ahead and fill in and T. Here. So M. T. Is going to be equal to And not and not it's going to be equal to and not times to raise the power of end but and not again is the initial number of cells. And notice that in the problem it tells us that we are starting from cells and so and not is going to be 10 and so we can go ahead and put 10 here for in and we'll go ahead and put this in parentheses just to isolate the end not here. So then we want to multiply and not by two raised to the power of N. And then again is going to be the number of new generations over a given amount of time. We can do that by taking the given amount of time. So if this is our equation, we want to calculate end, let's put in over here, just as an aside, if we want to calculate in, what we need to do is take the given amount of time, which is three hours, that's how much time is. Uh That's how much time they have to grow. And we want to convert that three hours into minutes so that the time units match each other, so the generation time is given to us in minutes. Uh and we have, the given amount of time is given to us in ours. So three hours is a total of 180 minutes, So and it's going to be equal to the given amount of time, which is three hours, 180 minutes divided by The generation time. And the generation time is given to us as 30 minutes. And so we can put 30 minutes here And so if you take your calculator and do 180 minutes divided by 30 minutes. What you'll get is that N. is equal to six. And so what we want to do is put a six here for our variable end. So taking a look at end here are end needs to be six and that's what we just calculated. So we'll go ahead and put a six year for variable end. And then all we need to do is crunch out the numbers. What we get is and T. Is equal to 10. And uh if we simplify this here to raise to the six power if you take that and type that into your calculator, what you'll get is that comes out to 64. So This 2-6 is equal to 64. And then if you take 64 and multiply it by 10 in your calculator. What you'll get is n.t. Is equal to 640. And so anti equaling 2 640 is matching with answer option D. Over here and so we can go ahead and mark that D. Is the correct answer for this example problem. And so what you can see here is that this uh equation can be used when you are given certain um variables. And by applying this equation you can calculate the number of cells after a given amount of time. And so we'll be able to get some practice applying this equation as we move forward. So I'll see you all in our next video.

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Problem

Problem

Calculate the number of cells that have grown after 12 hours starting from 100 cells that have a generation time of 1 hour.

A

40,960 cells

B

4,096 cells

C

4,096,000 cells

D

409,600 cells

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Problem

Problem

A microbiologist is having a population of 300 E. coli bacteria in an experiment in her lab. E. coli's generation time is 15 minutes. The scientist lets the E. coli population grow for 1 hour and 45 minutes. How many E. coli bacteria are present after this time?

A

29,700 cells

B

38,400 cells

C

600,000 cells

D

308,400 cells

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Problem

Problem

A microbiologist is studying the growth of Bacteria X. He allowed the population of Bacteria X to grow for 4 hours and 30 minutes, which resulted in 140,800 bacterial cells. The microbiologist realizes that he forgot to determine the size of his starting bacterial population. He knows that Bacteria X's generation time is 30 minutes, how many bacteria were in the starting population?