# 6.1 Exponential Growth and Decay Functions · PDF file 06.04.2018  · Tell whether each function represents exponential growth or exponential decay. Then graph the function. a) %!=2

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• Chapter 6 6.1 Exponential Growth and Decay Functions Exponential Growth and Decay Functions Definitions:

Exponential function: in the form of ! = #\$% where \$ ≠ 1 and must be positive. Exponential Growth: if # > 0 #+, \$ > 1 then ! = #\$% is an exponential growth function Exponential Decay: if # > 0 #+, 0 < \$ < 1 then ! = #\$% is an exponential decay function Growth/Decay Factor: the “b” value Asymptote: is a line that a graph approaches more and more closely. (Does not touch!)

Example 1: Graphing Exponential Growth and Decay Functions Tell whether each function represents exponential growth or exponential decay. Then graph the function.

a) ! = 2% b) ! = /0 %

Critical Thinking: You go out to eat at a nice restaurant and you receive the check. The check is for \$78 and you would like to leave a 20% tip. Calculate the total of the check and tip.

• Exponential Models Exponential Growth Model: ! = # 1 + 2 3 Exponential Decay Model: ! = # 1 − 2 3

*** IMPORTANT NOTE! When using a percentage “r” is always written in decimal form! ***

Example 2: Solving a Real-Life Problem The value of a car y (In thousands of dollars) can be approximated by the model ! = 25 0.85 3, where t is the number of years since the car was new.

a) Tell whether the model represents exponential growth or decay.

b) Identify the annual percent increase or decrease in the value of a car.

c) Estimate when the value of the car will be \$8,000. Example 3: Writing an Exponential Model In 2000, the world population was about 6.09billion. During the next 13 years, the world population increased by about 1.18% each year.

a) Write an exponential growth model giving the population y (in billions) t years after 2000.

b) Estimate the world population by 2005.

c) Estimate the year when the world population was 7 billion.

• Example 4: Rewriting an Exponential Function The amount y (in grams) of the radioactive isotope chromium-51 remaining after t days is ! = 0.5 3/09, where a is the initial amount (in grams). What percent of the chromium-51 decays each day? Compound Interest (We all love money!)

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