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Summary of Exponential and Logarithmic Functions

An Exponential Function is a function with a ________ in the __________ .. . . variable. exponent. Exponential Functions. . . . x. y. Domain:. All Real Numbers. Range:. All Positive Real Numbers. Exponential Decay. . . x. y. . Exponential Growth Curvereflected across the y-axis.. Growth

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Summary of Exponential and Logarithmic Functions

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    1. Summary of Exponential and Logarithmic Functions…

    2. An Exponential Function is a function with a ________ in the __________ .

    3. Exponential Functions

    4. Exponential Decay

    5. Growth Rate Formula:

    6. A Logarithm is an __________ .

    7. Exponential Form to Logarithmic Form

    8. Logarithmic Form to Exponential Form

    9. Logarithmic Functions

    10. Logarithm Properites

    11. Logarithm Properites

    12. Logarithm Properites

    13. ….SO, Now we can solve equations with a variable in the exponent…….

    14. How long will it take a population of 100 people to grow to 150 people with a 3% growth rate?

    15. How long…100 ? 150 @ 3% growth rate?

    16. How long…100 ? 150 @ 3% growth rate?

    17. Solving an Exponential Equation Divide FIRST! Simplify so the base raised to a variable = some number. Take the common log of both sides. Apply the power property to get the variable down out of the exponent. Then divide to solve for the variable.

    18. Solving Logarithmic Equations Use logarithm properties to simplify to get a single logarithm. (one side or both sides) If log A = log B, then A = B (Remove the logarithm from each side.) If log A = constant, then change from logarithmic form to exponential form and then solve.

    19. Solving Logarithmic Equations

    20. Solving Logarithmic Equations

    21. Solving Logarithmic Equations

    22. Orders of Magnitude see p. 323 The common logarithm of a positive quantity is its “order of magnitude”. Earthquakes – Richter Scale Sound Intensity – Decibels Ph scale for Chemical Acidity

    24. Newton’s Law of Cooling The object of a heated object will cool to the temperature of the medium into which it is placed, such as the air or water. T = Temperature T0 = Initial Temperature Tm = Temperature of medium t = time k = decay constant

    25. Newton’s Law of Cooling

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