6.1 Exponential Growth and Decay Functions · PDF file 06.04.2018 · Tell whether...

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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

Text of 6.1 Exponential Growth and Decay Functions · PDF file 06.04.2018 · Tell whether...

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.

*** 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!)