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Do Now:

Explore exponential growth and decay functions, their domains, ranges, and asymptotes. Learn about exponential models and how to apply them in real-life scenarios. Understand compound interest calculations and their impact on investments.

markcoffey
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Do Now:

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  1. Do Now: • Think about the function y = 2x. What do you think happens when x gets really big and positive? How about when x gets really big and negative?

  2. Do Now:

  3. Algebra II 6.1 Exponential Growth and Decay Functions

  4. Exponential Growth • An exponential function has the form y = abx where a ≠ 0 and b is a positive real number other than 1.

  5. Asymptote Exponential functions have asymptotes. An asymptote is a line that a graph approaches sooooo closely, but never touches.

  6. Exponential Growth Function If a > 0 and b > 1, then y = abx is an exponential growth function. We call b the growth factor.

  7. Domain: Range:

  8. Domain: Range:

  9. Exponential Decay Function If a > 0 and 0 < b < 1, then y = abx is an exponential decay function. We call b the decay factor.

  10. Domain: Range:

  11. Domain: Range:

  12. Exponential Models Some real-life quantities increase or decrease by a fixed percent each year (or some other time period).

  13. Exponential Models Exponential Growth Model y = a(1 + r)t Exponential Decay Model y = a(1 – r)t

  14. Exponential Models “a” is the initial amount “r” is the percent increase or decrease and is always written as a decimal “1 + r”/”1 – r” is the growth/decay factor.

  15. Example 2

  16. Example 3 In 2000, the world population was about 6.09 billion. During the next 13 years, the world population increased by about 1.18% each year. a. Write an exponential growth model giving the population y (in billions) t years after 2000. Estimate the world population in 2005.

  17. Example 3 Cont b. Estimate the year when the world population was 7 billion. Graph the model and use the table application.

  18. Example 4

  19. Compound Interest Compound interest is interest paid on an initial investment, called principal, and on previously earned interest.

  20. Compound Interest Compound interest is interest paid on an initial investment, called principal, and on previously earned interest. Interest earned is often expressed as an annual percent so we can use our growth model to help us in this economics application

  21. Compound Interest • Compound interest: interest paid on an initial investment, called principal, and on previously earned interest. • Interest earned is often expressed as an annual percent • Can use our growth model to help us in this economics application • However, interest is usually compounded more than once per year so we need to make a slight adjustment.

  22. Compound Interest

  23. Example 5 You deposit $9000 in an account that pays 1.46% annual interest. Find the balance after 3 years when the interest is compounded quarterly.

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