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Exponential Function Recap

Exponential Function Recap. Objective. Write and evaluate exponential expressions to model growth and decay situations. Recall, exponential growth occurs for base b > 1 and a positive exponent. Ex. or or or Pick out the base for each of these

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Exponential Function Recap

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  1. Exponential Function Recap

  2. Objective Write and evaluate exponential expressions to model growth and decay situations.

  3. Recall, exponential growthoccurs for base b > 1 and a positive exponent. Ex. or or or Pick out the base for each of these Exponential decayoccurs for base 0 < b < 1 and a positive exponent. Ex. or or or Pick out the base for each of these

  4. ALSO, Exponential decayoccurs for base b >1 and a negative exponent. Ex. or or or Pick out the base for each of these This is because using rules of exponents.

  5. Tell whether the function shows growth or decay. g(x) = 100(1.05)x h(x) = 5(1.2)-x

  6. You can model growth or decay by a constant percent increase or decrease with the following formula:

  7. In 2007, the Australian humpback whale population was 350 and increased at a rate of 14% each year since then. How many whales will there be in 2016. A(t) = a(1 +r)t Substitute for A(t), a, and r. Choose + because gaining population. A(9)= 350(1 + 0.14)(9) A(9)= ? Type into calculator exactly how it looks.350(1 + 0.14)(9)

  8. A city population, which was initially 15,500, has been dropping 3% a year. How many people will live in the city in 10 years? A(t) = a(1 – r)t A(10) = 15,500(1 – 0.03)10 A(t) = ?

  9. Logarithm Introduction

  10. Use mental math to evaluate. 1. 4–3 2. 2 because this means 3.10–2 4.

  11. Objectives Write equivalent forms for exponential and logarithmic functions. Evaluatelogarithmic functions.

  12. Vocabulary logarithm common logarithm logarithmic function

  13. Reading Math Read logby=x, as “the log base b of yis x.” Notice that the log is the exponent. The answer to a logarithm is the exponent. You can write an exponential equation as a logarithmic equation and vice versa. so log28=3 and sologby=x

  14. 1 1 log6 = –1 6 6 1 1 2 log255 = 2 Write each exponential equation in logarithmic form. log3243 = 5 log1010,000 = 4 logac =b

  15. 1 1 3 3 8 = 2 1 4–2 = 16 Write each logarithmic form in exponential equation. 91 = 9 29 = 512 1 16 b0 = 1

  16. A logarithm is an exponent, so the rules for exponents also apply to logarithms.

  17. A common logarithm has abase of 10. If no base is written for a logarithm, the base is assumed to be 10. For example, log 5 = log105.

  18. Evaluate by using mental math. log5 125 5?= 125 The log is the exponent. 53= 125 Think: What power of 5 is 125? log5125 = 3

  19. 1 1 1 5 5 5 5?= 5–1= 1 log5 = –1 1 5 5 Evaluate by using mental math. log5 The log is the exponent. Think: What power of 5 is ?

  20. 1 2 81 3 2. Change log279 = to exponential form. 2 27 = 9 3 1. Change 64 = 1296 to logarithmic form. log61296= 4 Calculate the following using mental math. 3. log 100,000 5 4. log648 5. log3 –4

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