1. The inaugural attendance of an annual music festival is 150,000. The attendance increases by 8% each year.

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1 NAME: DATE: Algebra 2: Lesson 11 7 Writing Exponential Growth and Decay Functions Learning Goals 1. How can we write an exponential growth/decay equation and define its variables? DO NOW: Answer the following questions in order to prepare for today s lesson. 1. Given the exponential functions below, identify the initial amount, the rate of change, and if it is growth or decay. a. ( ) ( ) b. ( ) ( ) Writing Exponential Growth and Decay Functions Exponential Growth Functions Exponential Decay Functions A function in the form ( ), where, is an exponential growth function. ( ) A function in the form ( ), where, is an exponential decay function. ( ) 1. The inaugural attendance of an annual music festival is 150,000. The attendance increases by 8% each year. Write an exponential function that represents the attendance after t years. How many people will attend the festival in the fifth year? Round your answer to the nearest thousand.

2 2. The value of a car is $21,500. Its value depreciates by 12% each year. Write a function that represents the value, in dollars, of the car after t years. Use this function to find how long it will take, to the nearest tenth of a year, for the car to be valued at $15, An apartment purchased 4 years ago for $80,000 was just sold for $105,000. Assuming exponential growth, approximate the annual growth rate, to the nearest percent.

3 Writing More Difficult Exponential Growth and Decay Functions What if the word problem does not give you the rate of change as a percent? Exponential growth look for keywords such as doubles, triples, quadruples,... Exponential decay look for keywords such as halves (half-life), a third, An initial population of 20 mice triples each year. Write an equation that models this population after t years. 5. The half-life of a medication is the time is takes for the medication to reduce to half of its original amount in a patient s bloodstream. A certain antibiotic has a half-life of one hour. A patient takes 500 milligrams of the medication. Write a function ( ) that models the amount of the medication in the patient s bloodstream over time. What if the word problem mentions the growth or decay rate over a specific period of time a. The half-life of a medication is the time is takes for the medication to reduce to half of its original amount in a patient s bloodstream. A certain antibiotic has a half-life of one hour. A patient takes 500 milligrams of the medication. ( ) ( ) b. The half-life of a medication is the time is takes for the medication to reduce to half of its original amount in a patient s bloodstream. A certain antibiotic has a half-life of about 3 hours. A patient takes 500 milligrams of the medication. ( ) ( )

4 6. Suppose that a water tank is infested with a colony of 1,000 bacteria. In this tank the colony doubles in number every 4 days. Determine a formula, ( ), for the number of bacteria present in the tank after t days. 7. Lead-209, a radioactive isotope, decays to nonradioactive lead over time. The half-life of lead-209 is 8 days. Suppose that 20 milligrams of lead-209 are created by a particle physics experiment. Write an equation for the amount of lead-209 present t days after the experiment. 8. Titanium-44 is a radioactive isotope such that every 63 years, its mass decreases by half. For a sample of titanium-44 with an initial mass of 100 grams, write a function that will give the mass of the sample remaining after any amount of time.

5 NAME: DATE: Algebra 2: Lesson 11 7 Writing Exponential Growth and Decay Functions Lesson 11-7 Exit Slip Directions: Answer the following question based on today s lesson. An adult takes 400 mg of ibuprofen. Every 2 hours, the amount of ibuprofen in the person s system decreases by 29%. Write a function that will give the amount of ibuprofen remaining after any amount of time. Use this function to predict the amount of ibuprofen remaining after 12 hours. Find the amount of time, to the nearest tenth of an hour, it will take for half of the ibuprofen to be left in a person s system.