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Analysis and Applications

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9 diapositives · 220 Views · Aug 15, 2014

In this guide, we explore the properties of logarithmic functions, including their domain, range, continuity, and asymptotic behavior. We analyze how each logarithmic function relates to the natural logarithm through stretching or shrinking. Additionally, we delve into the Richter scale, defining earthquake magnitude based on seismic wave features. Through step-by-step quality practice problems, we will compute earthquake magnitudes and evaluate intensity levels of light at specific depths. This comprehensive analysis aids in understanding key mathematical concepts and real-world applications.

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Analysis and Applications
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  1. Analysis and Applications in Section 3.4b

  2. Last class we discussed how the graph of every logarithm func. is a stretch or shrink of the graph of the natural logarithm func… Now let’s analyze our new function!!! Domain: Range: All reals (b, 1) Continuous Increasing on D (1, 0) No Symmetry Unbounded No Local Extrema No Horizontal Asymptotes E.B.: V.A.:

  3. Quality Practice Problems Graph the given function, and analyze it for domain, range, continuity, inc./dec. behavior, asymptotes, and end behavior. Domain: Range: Continuous Always Decreasing Asy: E.B.:

  4. Quality Practice Problems Graph the given function, and analyze it for domain, range, continuity, inc./dec. behavior, asymptotes, and end behavior. Domain: Range: Continuous Always Increasing Asy: E.B.:

  5. Quality Practice Problems The Richter scale magnitude R of an earthquake is based on the features of the associated seismic wave and is measured by where a is the amplitude in micrometers, T is the period in seconds, and B accounts for the weakening of the seismic wave due to the distance from the epicenter. compute the earthquake magnitude R for each set of values. (a)

  6. Quality Practice Problems The Richter scale magnitude R of an earthquake is based on the features of the associated seismic wave and is measured by where a is the amplitude in micrometers, T is the period in seconds, and B accounts for the weakening of the seismic wave due to the distance from the epicenter. compute the earthquake magnitude R for each set of values. (b)

  7. Whiteboard Problems… The relationship between intensity I of light (in lumens) at a depth of x feet in Lake Superior is given by What is the intensity at a depth of 10 ft? Plug in x = 10, solve for I: lumens

  8. Whiteboard Problems… Solve for x: Solve graphically!!!

  9. Whiteboard Problems… Solve for x: Solve graphically!!!