TenMarks teaches you how to solve application problems based on Exponents.
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Learn about Applications of Exponents In this track, let's learn about how do we practically apply what we've learned about exponents. The question says that in an office, an employee contacts three people. The three people in turn contact three other people. So every person is contacting three people and so on. How many people will be contacted by the end of the fifth round? So what do we know? We know that each employee contacts three people. We know that this goes on for five rounds. This is an exponent problem where the base equals the number of people contacted. The exponent equals the number of rounds. Let's solve this problem two different ways. First, let's assume that it's an exponential problem. So base is number of employees contacted, it's three and the exponent is number of rounds, it's five. So I can do a shortcut and say I can get to the answer by finding the value of 35 which is 3 x 3 x 3 x 3 x 3 which is 3 x 3 = 9 x 3= 27 x 3 = 81 x 3 = 243. You can put a multiplication sign. It's the same thing. So three multiplied by itself five times gives me the answer. The second way of doing it, that’s the first approach. The second approach is I can draw a tree. So there is the first employee. The first employee contacts three people. So that’s one, two and three. Now, each one of these employees contacts three more people. So, this person contacts three people. This person contacts three people. This person contacts three people. Now, each one of these, so the total number of people contacted at the end of round is three, at the end of round two is nine, at the end of round three, each one of these contacts three people each. So, each one of these will contact nine people. Each one of these will contact nine people. Each one of these will contact nine people which is 27. Do you see what I'm doing? Essentially each person contacts three now I have three of these so each one of these will contact three, each one of these three. So each of these ultimately these three will result in contacting nine. These nine will end up contacting 27. These nine will contact 27. These nine will contact 27. So the sum of these is 81. Now each one of these will contact three so, I'll get 81, 81, 81 which gives me 243. So at the end of round one, round two, round three, round four, round five I get 243 people which is what the answer was if I had simply put this in exponential form. So what have we learned? We've learned is if we know that we've got a problem where an employee contacts three people and this goes on five rounds, this is a classic exponent problem where I can write this problem as base and exponent where the base is number of times or number of people were contacted and this is the number of rounds. I can get to the answer which is 243 or I can do it by the three-method as well by looking at the first round second round, second round, third round, et cetera and I'll get to the same answer.