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Math 170 Functions, Data, and Models

Math 170 Functions, Data, and Models. 16 Exponential Functions Section 4.1. Population Change Examples. City A has 60 thousand people and is expected to increase by 10 thousand per year. What is its population after 1 year? 2 years? 3 years? years? 2.5 years?

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Math 170 Functions, Data, and Models

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  1. Math 170 Functions, Data, and Models 16 Exponential Functions Section 4.1

  2. Population Change Examples • City A has 60 thousand people and is expected to increase by 10 thousand per year. What is its population after 1 year? 2 years? 3 years? years? 2.5 years? • City B has 60 thousand people and is expected to increase by 10% per year. What is its population after 1 year? 2 years? 3 years? years? 2.5 years? • City C has 60 thousand people and is expected to decrease by 10% per year. What is its population after 1 year? 2 years? 3 years? years? 2.5 years? • Describe the shape of each population vs. time graph.

  3. Change Language • The plant grew from 4 cm to 6 cm tall this week! • What is the absolute change? relative change? percentage change? • Over one day, the amount of water in the jug dropped from 6 liters to 4 liters. • What is the absolute change? relative change? percentage change?

  4. Basic Concepts • A function is linear if it changes at a constant absolute rate. • is the initial value; is the rate of change • A function is exponential if it changes at a constant percentage rate. • is the initial value; is the growth factor; is the growth rate

  5. Investment Example • Suppose an investment earns a fixed return of 8% per year. Suppose you initially invest $500. What will your investment be worth years after the initial investment? • How long will it take to double the investment? • How long will it take to double the investment again?

  6. Bacteria Example • Suppose the population of bacteria (in millions) is after hours. • What is the initial population of bacteria? • What is the percent decrease per year?

  7. Folding Paper Example • How thick would a piece of paper that has been folded times be? • How many times could you fold a piece of paper?

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