Logarithmic Functions All slides in this

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Logarithmic Functions All slides in this presentations are based on the book Functions, Data and Models, S.P. Gordon and F. S Gordon ISBN 978-0-88385-767-0 Example 1 Consider the population of Niger, growing at rate 3.4 per year (one of

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Logarithmic Functions All slides in this presentations are based on the book Functions, Data and Models, S.P. Gordon and F. S GordonISBN 978-0-88385-767-0

Example 1 Consider the population of Niger, growing at rate 3.4% per year (one of the fastest in the world)

Population growth of Niger - Graph This exponential function is strictly increasing so for we know that there is exactly one time value for which P(t) = 18. How to find it algebraically?

Definition of Logarithm with Base 10

Example solving equations using logarithms Solution

Example solving equations using logarithms Example 2 Determine algebraically when the population of Niger will reach 18 million. Solution

Example solving equations using logarithms Example 3 Determine the half life of ibuprofen in blood given it follows the decay model Solution The level of ibuprofen in your blood will drop by half in just under two hours.

Behavior of the Logarithmic Function Some questions:
What is the domain?
What is the range?
For what values of x is the function increasing (decreasing)?
For what values of x is the function concave up (concave down)?

Additional Properties of Logarithms

Comparing Exponential and Logarithmic Functions

Modeling with Logarithms

Earthquakes and the Richter Scale

Earthquakes and the Richter Scale The largest recorded earthquake, which occurred in Chile in 1960, had a magnitude R = 9.5 on the Richter scale.

This quake had an intensity more than 3.1 billion times greater than the threshold level.

Earthquake Example Example 2 How does a magnitude 6 earthquake on the Richter scale compare to a magnitude 5 earthquake?
Solution If R = 5 we have If R = 6 we have The intensity of a magnitude 6 earthquake is 10 times greater than the magnitude 5 earthquake.

Sound Decibels

Sound Decibel Example The intensity of normal conversation is 1,000,000 times the threshold level.

Logarithmic Functions All slides in this

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