Exponential Functions, Growth, and Decay (2 Questions)

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# Exponential Functions, Growth, and Decay (2 Questions) - PowerPoint PPT Presentation

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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Presentation Transcript
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)
• Write the exponential in logarithmic form:
• 3. 35 =343
• Write the logarithmic in exponential form:
• 4. 2 = logo.6 0.36
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

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
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.

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.

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.