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Section 6.1 – Exponential Functions

Section 6.1 – Exponential Functions. Exponential Functions. An exponential function is a function that can be written in the form , where and are real numbers and. 1. 1/16. 1/8. 1/4. Exponential growth. 1/2. 1. 2. 4. 8. 16. Exponential Functions. 2. 16. 8. Exponential decay.

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Section 6.1 – Exponential Functions

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  1. Section 6.1 – Exponential Functions

  2. Exponential Functions An exponential function is a function that can be written in the form , whereand are real numbers and. 1. 1/16 1/8 1/4 Exponential growth 1/2 1 2 4 8 16

  3. Exponential Functions 2. 16 8 Exponential decay 4 2 1 1/2 1/4 1/8 1/16

  4. Exponential Functions • Continuous • One – to – One • Domain: • Range: • , graph increases • , graph decreases • x-axis is a horizontal asymptote • y-intercept:

  5. Exponential Functions – growth/decay rate : initial value : growth factor : exponential growth : exponential decay Determine whether the function represents exponential growth or exponential decay. State the initial value and growth/decay rate. 4. 3. Exponential decay Initial Value: decay rate: Exponential growth Initial Value: growth rate:

  6. Exponential Functions While linear functions have a constant rate of change, exponential functions have a constant percentage change. For equally spaced inputs, we determine percent change in outputs by

  7. Exponential Functions 5. Determine whether the table could represent a function that is linear, exponential or neither. Exponential Decay Decay Rate:

  8. Find the exponential function Find the formula for the exponential function that passes through the two points given. and

  9. Find the exponential function Find the formula for the exponential function that passes through the two points given. and Set up a ratio:

  10. Find the exponential function Find the formula for the exponential function that passes through the two points given. and Use point:

  11. The Number e The number e is a non-terminating, non-repeating decimal. Use your calculator to approximate the following to four decimal places: 8. 9.

  12. The Number e

  13. The continuous growth/decay function : initial value : continuous growth rate : exponential growth : exponential decay Determine whether the function represents exponential growth or exponential decay. State the initial value and the continuous growth/decay rate. 11. 10. Exponential decay Initial Value: continuous decay rate: Exponential growth Initial Value: continuous growth rate:

  14. Compound interest account balance principal annual rate, in decimal form # of compounding periods per year time, in years

  15. Compounded times 12. Find the account balance.

  16. Compounded times 13. Find the account balance.

  17. textbook problems Textbook - p. 476: 15, 17, 18, 20, 23, 26, 28, 29, 31, 39, 41, 45

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