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Exploring Exponential Growth and Decay Models in Real-World Scenarios

This document examines the United States population data from 1980 to 1986 to analyze potential linear and exponential relationships. It also includes practical examples of exponential growth and decay: calculating house appreciation over years using a 2.3% annual increase, determining bacterial growth from an initial population of 10,000 at 1% per hour, and evaluating the depreciation of a car costing $18,000 at an annual rate of 18%. These analyses provide insights into modeling real-life situations with exponential functions.

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Exploring Exponential Growth and Decay Models in Real-World Scenarios

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  1. Exponential Functions 1.4

  2. Bellwork Page 24 #18

  3. Listed in the table below is the United States population data for the years 1980 to 1986. Is there a linear relationship? Is there another relationship within the data?

  4. Exponential Growth model Exponential Growth Exponential Decay

  5. A house was purchased in 1998 for $106,000. If houses in that area appreciate approximately 2.3% per year, what is the value of the house in 2010?

  6. Suppose that an initial population of 10,000 bacteria grows exponentially at a rate of 1% per hour. Find a formula that represents the number of bacteria present t hours later.

  7. A certain model car depreciates approximately 18% per year. When new, the cost of the car was $18,000. What is the value of the car in 5 years?

  8. Homework Page 31 #7, 9-13 odd, 14-18 all, 21

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