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Exponential Functions, Growth, and Decay (2 Questions)

Exponential Functions, Growth, and Decay (2 Questions). Tell whether each function represents growth or decay, then graph by using a table of values: 1. 0.5(1.25) x. Inverses (3 questions). Write the inverse of the following function: 2. . Logarithmic functions (4 questions).

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Exponential Functions, Growth, and Decay (2 Questions)

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  1. Exponential Functions, Growth, and Decay (2 Questions) • Tell whether each function represents growth or decay, then graph by using a table of values: • 1. 0.5(1.25)x

  2. Inverses (3 questions) • Write the inverse of the following function: • 2.

  3. Logarithmic functions (4 questions) • Write the exponential in logarithmic form: • 3. 35 =343 • Write the logarithmic in exponential form: • 4. 2 = logo.6 0.36

  4. Properties of logarithms (6 questions) • Express as a single logarithm and simplify • 5. log2 8+ log2 16 • 6. log 10 – log 0.1 • 7. ln e4x 8. e4 lnx • 9. log 1064 – 2(10log 16) log2 16

  5. Exponential and Logarithmic Equations (4 questions) • Solve: • 10. 3x-1 = 1/9 11. 5x = 50 • 12. 2x+4 = 20 • 13. log (x – 2) + log (x + 2) = 21

  6. The natural Base, e (4 questions, overlapping with properties of logs) • Simplify: • 14. eln(2x+1) 15. ln e14x • 16. Use the natural decay function: N(t) = N0e-kt to find the age of a fossil containing 30% of the original amount of a substance whose half life is 5000 years.

  7. Transformations (2 questions) • 17. Write the transformed function: f(x) = log (x – 1) is translated 5 units right at then reflected across the x-axis. • Write the transformed function: f(x) = ex is reflected across the x – axis, stretched vertically by a factor of 3, and shifted 2 units down.

  8. Exponential and Logarithmic Regressions (2 questions) • The table gives the population size of a flock of birds in one habitat over the last 55 years. • Find an exponential regression for the data.

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