Objective: Use exponential and logarithmic models to solve real life problems. 3.5 Exponential & Logarithmic Models 2014.

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Presentation transcript:

Objective: Use exponential and logarithmic models to solve real life problems. 3.5 Exponential & Logarithmic Models 2014

Exponential Models Exponential Growth Model: Exponential Decay Model: Logistic Growth Model: Logarithmic Models:

Exponential Model Exponential Growth/ Decay Model:

Investment Example Complete the table for a savings account in which interest is compounded continuously: Initial InvestmentAnnual % RateTime to DoubleAmount After 10 Years $20, % $10,00012 years

Population Growth Example The population of Higley is given by the exponential equation where P is in thousands and t=0 represents the year In 1980 the population was 74,000. Find K, and then use the equation to predict the population in 2020.

describes the number of bacteria in a culture after t hours. If n=400 when t=3, find the time required for the bacteria to double. Bacteria Growth

Modeling Population Growth A population of fruit flies follows the exponential growth function. After 2 days there are 100 flies and after 4 days there are 300 flies. Find the growth model, and then use it to find out how many flies there will be after 5 days?

You try: A population of bacteria on your desk follows the exponential growth function (in thousands). After 2 days there are 4 (thousand) bacteria on your desk and after 4 days there are 20 (thousand) bacteria on your desk. Find the growth model, and then use it to find out how much bacteria there will be on your desk in 7 days.

Radioactive Decay A certain radioactive isotope has a half life of 1200 years. If the initial quantity is 20 grams, use an exponential model to determine how much remains after 1000 years.

Radioactive Decay The half-life of radioactive Plutonium is 24,100 years. What percent of a present amount of radioactive strontium will remain after 50,000 years?

Spread of a Virus On a college campus of 5000 students, one student returns from vacation with a contagious flu virus. The spread of the virus is modeled by where y is the total number infected after t days. The college will cancel classes when 40% or more of the students are infected. a) How many students are infected after 5 days? b) After how many days will the college cancel classes?

Sales The sales S (in thousands of units) of a cleaning solution after x hundred of dollars is spent on advertising are given by: When $500 is spent on advertising, 2500 units are sold. a) Complete the model by solving for k. b) Estimate the number of units that will be sold if advertising expenditures are raised to $700.

Logarithmic Model On a Richter scale, the magnitude R of an earthquake of intensity I is given by where is the minimum intensity used for comparison. Intensity is a measure of the wave energy of an earthquake. In 2001, the coast of Peru experienced an earthquake that measured 8.4 on the Richter scale. In 2003, Colima, Mexico experienced an earthquake that measured 7.6 on the Richter scale. Find the intensity of each earthquake and compare the two intensities.

Homework 3.5 pg , 19-25, 28, 29, 31 ALL ODDS