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# lecture26 - Math 121 Lecture 26 Chapter 5 Applications of...

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Chapter 5 Applications of the Exponential and Natural Logarithm Functions Math 121 Lecture 26 ! Exponential Growth and Decay ! Compound Interest ! Applications of the Natural Logarithm Function to Economics

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§ 5.1 Exponential Growth and Decay ! Exponential Growth ! The Exponential Growth and Decay Model ! Exponential Growth in Application ! Exponential Decay ! Exponential Decay in Application
Definition Example Exponential Growth : A quantity, such that, at every instant the rate of increase of the quantity is proportional to the amount of the quantity at that instant

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( World’s Population ) The world’s population was 5.51 billion on January 1, 1993 and 5.88 billion on January 1, 1998. Assume that at any time the population grows at a rate proportional to the population at that time. In what year will the world’s population reach 7 billion? Since the “oldest” information we’re given corresponds to 1993, that will serve as our initial time. Therefore the year 1993 will be the year t = 0 and the population at time t = 0 is 5.51 (measured in billions). Therefore, the year 1998 will be year t = 5 and the population at time t = 5 is 5.88 (measured in billions). Since the population grows at a rate proportional to the size of the population,
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lecture26 - Math 121 Lecture 26 Chapter 5 Applications of...

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