Simplify the following expressions Simplify the following expressions Graph the following functions Classify each as growth or decay Solve the following equations Find an exponential equation that contains the given points ID: 779453
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Slide1
Chapter 4 Review
Exponential Functions
Slide2Simplify the following expressions
Slide3Simplify the following expressions
Slide4Graph the following functions. Classify each as growth or decay.
Slide5Solve the following equations
Slide6Find an exponential equation that contains the given points
(0, 12.94) and (20, 357.03)
(2, 73.8) and (7, 13.2)
Slide7Using data described in words
Suppose a rumor is spreading that the US government plans to give each college student $2000. Assume that 40 people have heard the rumor as of today and that each day the number of people (past and present) who have heard it triples. Let f(t) be the number of people (past and present) who have heard the rumor at
t
days since today.Find an equation of f.How many people (past and present) will have heard the rumor 10 days from now?How many people will have heard the rumor 15 days from now? Has model breakdown occurred? Assume that the US population is 306 million.
Slide8Using data described in words
A person invests $7000 at 10% interest compounded annually. Let f(t) be the value (in dollars) of the account at
t
years after he has deposited the $7000.Find an equation of f.What is the base b of your model? What does it mean in this situation?What is the coefficient a? What does it mean in this situation?What will be the account’s value in 10 years?
Slide9Using data described in words
Laser disc player sales were $108 million in 1995. Sales approximately halved each year from 1995 to 1999. Let f(t) be the sales (in millions of dollars) for the year that is
t
years since 1995.Find an equation of f.What is the y-intercept of the model? What does it mean in this situation?Find f(4). What does it mean in this situation?
Slide10Half-Life
A physician injects a patient with thallium-201 to determine how well blood flows to the patient’s heart muscle. Thallium-201 has a half life of 2.3 days. Let f(t) be the percentage of the thallium-201 that remains in the patient’s body at
t
days since she was injected.Find an equation of f.What percentage of thallium-201 will remain after 5 days?
Slide11Using data described in words
A growing number of thieves are using keylogging programs to steal passwords and other personal information from Internet users. The number of keylogging programs reported grew approximately exponentially from 0.2 thousand programs in 2001 to 12.0 thousand programs in 2006. Predict the number of keylogging programs that will be reported in 2014.
Slide12Using data described in a table
A person’s heart attack risk can be estimated by using Framingham point scores, which are based on such factors as age, cholesterol level, blood pressure, and smoking habits. Men’s risks of having a heart attack in the next 10 years are shown in the table for various scores. Let
f(s)
be a man’s risk of having a heart attack in the next 10 years if his score is s points.Find an equation of f.A 47 year old man has a score of 11 points. What is the risk that he will have a heart attack in the next 10 years?Framingham Point ScoresRisk (percent)015210615201730