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Section 10.7:

Section 10.7:. Exponential Curve Fitting and Other Applications of Exponential and Logarithmic Equations. 10.7 Lecture Guide: Exponential Curve Fitting and Other Applications of Exponential and Logarithmic Equations.

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Section 10.7:

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  1. Section 10.7: Exponential Curve Fitting and Other Applications of Exponential and Logarithmic Equations

  2. 10.7 Lecture Guide: Exponential Curve Fitting and Other Applications of Exponential and Logarithmic Equations Objective: Use exponential and logarithmic equations to solve applied problems.

  3. Growth and Decay Formulas Periodic Growth Formula Verbally The amount A that is produced by an original amount P growing at an annual rate r with periodic compounding n times a year for t years. Algebraic Example This is the amount resulting from investing $1000 at 7% compounded quarterly for 10 years.

  4. Growth and Decay Formulas Continuous Growth and Decay Formula Verbally The amount A that is produced by an original amount P growing (decaying) continuously at a rate r for a time t. If r > 0 there is growth. If r < 0 there is decay. Algebraic Example This is the amount resulting from investing $1000 at 7% compounded continuously for 10 years.

  5. 1. Compute the value of $10,000 invested at 8% for 5 years if interest is compounded: (b) Quarterly (a) Semiannually

  6. 1. Compute the value of $10,000 invested at 8% for 5 years if interest is compounded: (d) Daily (c) Weekly

  7. 1. Compute the value of $10,000 invested at 8% for 5 years if interest is compounded: (e) Continuously

  8. 2. How many years will it take an investment of $500 to triple in value if interest on the investment is compounded monthly at a rate of 9%?

  9. 3. Since the population of Springfield was last given to be 35,000 residents in 2000, it has been growing at a rate of 2.75% per year. (a) Give a function to model the population of Springfield since 2000.

  10. 3. Since the population of Springfield was last given to be 35,000 residents in 2000, it has been growing at a rate of 2.75% per year. (b) Use this function to estimate the population in 2010.

  11. 3. Since the population of Springfield was last given to be 35,000 residents in 2000, it has been growing at a rate of 2.75% per year. (c) Using this growth rate determine when the population will be 50,000 residents.

  12. 4. A swab of a kitchen counter revealed 8000 bacteria. This bacteria sample was found to grow at a continuous rate of 18% per hour when placed in an incubator. If the bacteria sample was placed in an incubator for 24 hours, how many bacteria will be present at the end of the period?

  13. 5. Use the formula to determine the magnitude of an earthquake on the Richter scale that measured 50,000 . times the reference amplitude

  14. 6. The intensity of the music at a concert was measured at Use the formula . to determine the decibel reading at this concert.

  15. 7. Use the formula to determine , the concentration of hydrogen ions in moles per liter of orange juice given that the for orange juice is 3.8.

  16. 8. Use a graphing calculator and the points given in the table to (a) Draw a scatter diagram of these points.

  17. 8. Use a graphing calculator and the points given in the table to (b) Determine the exponential function that best fits these points. Round the coefficients to three significant digits.

  18. 8. Use a graphing calculator and the points given in the table to (c) Use this equation to estimate y when x is 2.5.

  19. 8. Use a graphing calculator and the points given in the table to (d) Does this function represent exponential growth or exponential decay?

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