Exponential Growth and Decay

# Exponential Growth and Decay - Exponential Growth(k > 0 A...

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Exponential Growth , ( k > 0)

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A represents the amount at a given time t . A o represents the initial amount of the growing entity. Note that this is the amount when t = 0. k is a constant that represents the growth rate. It is POSITIVE when talking in terms of exponential GROWTH. t is the amount of time that has past. If the information for time is given in dates, you need to convert it to how much time has past since the initial time. For example, if the model is set up at an initial year of 2000 and you need to find out what the value is in the year 2010, t would be 2010 - 2000 = 10 years. You can use this formula to find any of its variables, depending on the information given and what is being asked in a problem. For example, you may be given the values for A o and t and you need to find the amount A after the given time. Or, you may be given the final amount A and the initial amount A o and you need to find the time t . Some examples of exponential growth are population growth and financial growth. The information found, can help predict what a population for a city or colony would be in the future or what the value of your house is in ten years. Or you can use it to find out how long it would take to get to a certain population or value on your house. The diagram below shows exponential growth:
Example 1 : The exponential growth model describes the population of a city in the United States, in thousands, t years after 1994. Use this model to solve the following: A) What was the population of the city in 1994? B) By what % is the population of the city increasing each year? C) What will the population of the city be in 2005? D) When will the city’s population be 60 thousand? A) What was the population of the city in 1994? Since we are looking for the population, what variable are we seeking? If you said A you are right on!!!! The way the problem is worded, 1994 is what we call our initial year. This is when t = 0. Plugging in 0 for

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Exponential Growth and Decay - Exponential Growth(k > 0 A...

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