8.1& 8.2 Exponential Growth and Decay Functions EQ1: What do we need to know about the graphs of exponential functions? EQ2: How can we tell the difference between growth and decay problems?

EQ: How can we tell the difference between growth and decay problems? Exponential Models Growth: Decay: y = final amount P = initial amount t = time in years r = % of increase 1+r = growth factor y = final amount P = initial amount t = time in years r = % of decrease 1- r = decay factor EQ: How can we tell the difference between growth and decay problems?

EQ: How can we tell the difference between growth and decay problems? Basically… If the number raised to a power is GREATER than 1, then it is a GROWTH function. If the number raised to a power is LESS than 1, then it is a DECAY function. The growth/decay factor is the number raised to a power! EQ: How can we tell the difference between growth and decay problems?

EQ: How can we tell the difference between growth and decay problems? In 2005, the cost of tuition at a state university was $6,000. During the next 5 years, the tuition is expected to rise 4% each year. Write a model the gives the tuition y (in dollars) t years after 2005. What is the growth factor? How much would it cost to attend college in 2008? In 2010? EQ: How can we tell the difference between growth and decay problems?

EQ: How can we tell the difference between growth and decay problems? A certain car depreciates at a rate of 11% per year. It was purchased new in 2006 for $32000. Write a model the gives the value of the car y (in dollars) t years after 2006 What is the decay factor? How much is the car worth now? In 2012? Estimate the year the car be worth approximately $4560. EQ: How can we tell the difference between growth and decay problems?

Compound Interest $ For n compoundings per year: You need to know this box!! A = balance (final amount) P = principle (initial amount) t = time in years r = annual interest rate – DECIMAL form n = times compounded per year $

a) quarterly b) monthly A total of $ 12,000 is invested at an annual interest rate of 9%. Find the balance after 5 years if it is compounded a) quarterly b) monthly = $18,726.11 = $18,788.17 $

Homework Day 1: pg. 469 #19-24 all; 26-42 even; 43-45, 49-51, and 59-61 all Day 2: Pg. 477 #19-24 all; 43-55 all; 67