Math 1320 Chapter 9: Nonlinear Functions and Models 9.3 Logarithmic Functions and Models.

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Presentation transcript:

Math 1320 Chapter 9: Nonlinear Functions and Models 9.3 Logarithmic Functions and Models

Definition

Examples: Rewrite in the opposite form.

Change of Base Formula

Examples: Use logarithms to solve

Logarithmic Identities

Examples How long will it take a $500 investment to be worth $700 if it is continuously compounded at 10% per year? Round to the nearest tenth of a year. How long, to the nearest year, will it take an investment to triple if it is continuously compounded at 12% per year?

Definitions

Examples Find the associated exponential growth or decay function. 1.Q = 1000 when t = 0; half-life = 3 2.Q = 2000 when t = 0; doubling time = 2 3.Q = 35 when t = 0; doubling time = 1.5

Examples

Example Soon after taking an aspirin, a patient has absorbed 300 mg of the drug. If the amount of aspirin in the bloodstream decays exponentially, with half being removed every 2 hours, find, to the nearest 0.1 hours, the time it will take for the amount of aspirin in the bloodstream to decrease to 100 mg.

Example After a large number of drinks, a person has a BAC of 200 mg/dL. If the amount of alcohol in the blood decays exponentially, with one fourth being removed every hour, find the time it will take for the person’s BAC to decrease to 80 mg/dL.