Learn about Powers and Exponents Applications In this lesson, let's learn how we apply powers and exponents to real lief problems. The problem we will work to as a sample says the following; a certain bacterium divides into two bacteria every hour. So there is a singular bacterium that divides into two bacteria every hour. There is one bacterium to start with on a slide. So, we start with one bacterium. This is what we have. If it divides every hour, how many will we have after six hours? So in one hour, what do I get? I get one B. This divides into two bacteria. This divides into two bacteria. So this is at one hour. What happens at two hours? Well, this one divides into two. One bacterium divides into two and this one divides into two. So taking some more space; after two hours, I get this. What about after three hours? Well this one will divide into two. This one will divide into two. This divides into two and this divides into two. So, we’ll have all of these bacteria. So this is three hours. This is two hours. This is one hour. And this goes on. Could see a trend here? So, this is zero. At one hour, what do I have? I have two. At hours, one, two, three, four. At three hours, one, two, three, four, five, six, seven, eight. What is this number? Well this is 21 or base 2, exponent 1. This is base 2, exponent 2. This is base 2, exponent 3. Two with an exponent 3 is 2x2x2 which is 8. So as we can see, three hours gives us base 2, exponent 3. Two hours gives us base 2, exponent 2. So after N hours, what will we have? We will have two with an exponent N. So now that we figured out the pattern to this, let's figure out what are they trying to say. We need to find how many bacteria will be on the slide after six hours. So I can do this. So after six hours, what will I have? After six hours, what will I have? 26 or 2 with an exponent of 6; that is 2x2x2x2x2x2, that’s 4, 8, 16, 32, 64. So at the end of six hours, I will have 64 bacteria on the slide. How did we get this? All we did is we started drawing it out and we noticed that there was a pattern. And the pattern was that it is a base of 2 and exponent one, two, three corresponding to one, two, three hours. So for six hours, we will have a base of 2, exponent 6 to the power six, which is 64.