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© The Algebros from FlippedMath.com QUICK REVIEW Remember that logarithmic functions have independent values that increase proportionally while the dependent values increase at a constant rate. *The amount the proportional values increase of the independent values would also be the base. Ex 1: At the end of the school year, the classroom gets really warm! As the number of students increases so does the temperature. Mr. Bean took some data last May! What’s a regression equation to model the situation: What’s the temperature if there are 35 students? How many students are there when the temperature reaches 85 degrees? Ex 2: Mr. Kelly loves to wake up and have a fresh cup of coffee. He likes his coffee to cool down a bit though before drinking it. He makes a table of values to help him find an appropriate model. He sets his data up so that the time (in minutes) is a function of the temperature (in degrees). Find a regression equation to model the equation: How long will it take for Mr. Kelly’s morning coffee to be 70 degrees? 2.14 Logarithmic Function Context and Data Modeling Write your questions and thoughts here! AP Precalc 2.14 Notes

© The Algebros from FlippedMath.com Ex 3: People measure loudness in terms of decibels using the following function, where D(I) is the decibel level, I is the intensity of the sound and 10 -12 is the intensity of the quietest sound a human can hear. What’s the intensity of the sound of the school fire alarm is if registers as 100 decibels? Ex 4: Mr. Brust wants to save for a new Lamborghini. He currently has $50,000 in an account that pays interest continuously and will need to save $300,000 in total. If he saves money for 12 years, what interest rate would he need to achieve his goal? Use the equation below where A(t) is the current amount of money, P is the principal (starting value), r is the interest rate and t is the time in years. ࠵?(࠵?) = ࠵?࠵? !" 2.14 Logarithmic Function Context and Data Modeling AP Precalculus Calculator Active: Instructions: Use the data provided to find a regression equation and answer the questions. 1) Mr. Bean started learning Chinese in hopes of translating all his videos one year. He created some data to find a model for the number of days studying as a function of the number of words he learned that day. a) What’s a logarithmic regression equation that could model this situation? b) How many days would it take for Mr. Bean to learn 1000 words? c) How many words would he learn if he studied for 2 months (60 days)? 2.14 Practice Write your questions and thoughts here!

© The Algebros from FlippedMath.com 2) Mr. Sullivan recently decided (with the help from his doctor) that he needed to start a diet. Each week he collects data on the amount of weight he loses that week. He wants to find a regression equation that models the pounds lost on a particular week as a function of the week number. a) What’s a logarithmic regression equation that could model this situation? b) Which week number will Mr. Sullivan lose 2 pounds? c) How many pounds will Mr. Sullivan lose during the 12 th week? Week # 1 2 6 9 Pounds Lost that week 9.5 8.5 6.5 5.5 3) The latest and greatest new tech firm, Math Geek Tech, is about to go public on the Stock Exchange. The market guys at Math Geek Tech want to create a regression model that shows the stock price (in dollars) as a function of the number of days on the market. a) What’s a logarithmic regression equation that could model this situation? b) How many days will it take for the stock price to be $250? c) What would the stock price be after the first two weeks on the market (14 days)? Days on Market 1 3 4 7 Stock Price($) 112 150.5 160.5 180.1

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© The Algebros from FlippedMath.com Calculator Active: Instructions: Use the information given to answer the questions. Round to nearest thousandth. 4) People can use the formula below to determine future populations ( N(t)) of cities. N 0 represents the initial population, r is the rate of population growth, and t is the time in years. ࠵?(࠵?) = ࠵? # ࠵? !" a) What would the population be of Cleveland, Ohio be in 10 years if there are currently 275,000 people, with a population growth rate of 2.5%. b) What growth rate would Cleveland, Ohio need to achieve a population of 400,000 people in 20 years? 5) Forensics often use Newton’s Law of Cooling to determine the elapsed time since a person has died. The formula is ࠵? = −10 ln ( !"# $%.’"# ) , where T stands for the body’s temperature in degrees Fahrenheit, R is the temperature of the room and t is the elapsed time since death in hours. a) How many hours had elapsed if the temperature of the room was 75 o and the body’s temp was 85 o ? b) Suppose a body found 5 hours after death (neighbor heard thud) in a room that was 65 o . What was the temperature of the body? 6) The table presents values for a function, f, at selected values of x. A logarithmic regression is used to model the data. What is the value of f(4.5)? (A) 35.225 (B) 34.987 (C) 54.639 (D) 54.012 x F(x) 1 44.9 3 37.9 7 32.4 9 30.7 2.14 Test Prep 2.14 Logarithmic Function Context and Data

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