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7.5 Modelling Data Using

Logarithmic FunctionsPages 488 ­ 499

Review:Laws of exponents­

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Since logarithms are exponents, they also have similar laws:

1. Product Law ­

2. Quotient Law ­

3. Power Law ­

**Note: We will apply law #3 to various problems to calculate the result algebraically.

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Graphical Approach to Solving Logarithmic Functions:

Page 488

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Answers

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(Select STAT, CALC, and 9:LnReg)

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Page 489

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Example 1(Algebraically): Using the power law of logarithms and exponential function, calculate the t.5 flash duration given a rate of decrease of 18.13%/.02s.

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Page 491

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Example 2(Algebraically): Using the power law of logarithms and exponential function, repeat b) and c) given a rate of decrease of 11%/h.

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Page 493

Determine the solution:a) Graphically using the logarithmic regression for example 2.b) Algebraically using the determined exponential equation and the power law of logarithms.

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Additional Exercises:Using the exponential function determined and the power law of logarithms redo the following exercises from section 7.3 and 7.5. Compare with previously found answers.

Section 7.3#5 page 462­ Rate of increase 16% per 10 years; repeat d)

# 6 page 462­ Growth rate of 60% per 7 years; repeat d)

#9 page 463­ Rate of decrease 20% per year; repeat c)

#11 page 464 ­ Decay rate of 5% per minute; repeat b)

#14 page 465­ Growth rate 10% per week; repeat b)

#17 page 467­ Rate of decrease is 3% per gel; repeat c)

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Section 7.5 (determine the exponential equation first)#5 page 496­ Rate of decrease 0.02% per metre; repeat d) and e)

#6 page 497­ rate of decrease is 50% per 5760 years with initial percent of 100%; repeat b)

#7 Page 497­ rate of increase is 4.5%/year; repeat c)