Skill 14: Applying Exponential Functions to Real-World Scenarios

With the Person Next to You… According to U.S. Census Bureau estimates, the city of Charlotte, North Carolina, had a population of approximately 687,000 in Assuming that the population increases at a constant percent rate of 3.0%, determine the population of Charlotte (in thousands) in Determine the population of Charlotte (in thousands) in Divide the population in 2009 by the population in 2008 and record this ratio. Divide the population in 2010 by the population in 2009 and record this ratio. What do you notice about the ratios in parts c and d? What do these ratios represent?

Applying Exponential Functions Linear functions represent quantities that change at a constant average rate (slope). Exponential functions represent quantities that change at a constant ___________________________ rate.

Writing an Exponential Function for a Given Situation Population growth, sales and advertising trends, compound interest, spread of disease, and concentration of a drug in the blood are examples of quantities that increase or decrease at a constant percent rate.

You Try: Identify each situation as growth or decay. 1.On the Biggest Loser television show, contestants lose 5% of their body weight every week. 2.After winning two games in a row, the Indy Eleven soccer team’s stadium attendance has increased by 1% for each game. 3.My Microsoft stock (MSFT) has been doing poorly, and I’ve been losing 8% of its value every day.

Writing an Exponential Function for a Given Situation Example #1: Write the exponential function that models the population growth for Charlotte, North Carolina. What is the current (2014) population of Charlotte, North Carolina, according to our model? How long will it take for the population of Charlotte, North Carolina to double?

Writing an Exponential Function for a Given Situation Example #2: You are working at a wastewater treatment facility. You are presently treating water contaminated with 18 micrograms of pollutant per liter. Your process is designed to remove 20% of the pollutant during each treatment. Your goal is to reduce the pollutant to less than 3 micrograms per liter. a) Write the exponential function that models the pollutant level in this water. b) How many micrograms of pollutant are in the water after 5 treatments?

Writing an Exponential Function for a Given Situation Example #3: You have recently purchased a new car for $20,000 by arranging financing for the next 5 years. You are curious to know what your new car will be worth when the loan is completely paid off. a) Assuming that the value depreciates at a constant rate of 15%, write an equation that represents the value of the car x years from now. b) How much will the car be worth when the loan is paid off?

You Try:

Applying the Compound and Continuous Interest Formulas The interest paid on savings accounts in most banks is compound interest. The interest earned for each period is added to the previous principal before the next interest calculation is made. Simply stated, interest earns interest.

Applying the Compound and Continuous Interest Formulas The formula for compounding interest is

Applying the Compound and Continuous Interest Formulas Example #4: You invest $100 at 4% compounded quarterly. How much money do you have after 5 years?

You Try: You invest $25,750 at 6% compounded twice a year. How much money do you have after 4 years?

Applying the Compound and Continuous Interest Formulas

Exit Quiz 1.The number of students at Herron High School increases at a constant rate of 28% each year. Herron started with 80 students. How many students will Herron have 15 years after opening? 2.At age 11, I invested $600 in a savings account that pays 1% interest compounded monthly. How much money do I have in my account, now that I am 31 years old?