9.3 Expo growth decay comp.notebook
March 22, 2017
On your graphing calculator or DESMOS graph
and Use a window of [0,4] for your ‘x’ values and [0,15] for your ‘y’ values. Discuss with your group what you see.
Sketch the two graphs in your notes, make sure you label each graph.
Jan 26­9:01 PM
9.3 Expo growth decay comp.notebook
March 22, 2017
9.3 Exponential Growth and Decay
Definition
For a>0 and b>0, the function
y=a(b)x OR a=starting amount
b=decay factor if 0<b<1
b=growth factor if b>1
x=# of increases
y=a(1+r)x
r<0 decay
r>0 growth
Jan 26­9:01 PM
9.3 Expo growth decay comp.notebook
March 22, 2017
Ex.1 If y=5(0.95)x a) What is the initial amount?
b) Is the function exponential growth or decay?
c) What is the growth/decay factor?
d) What is the percent of increase/decrease?
Jan 26­9:01 PM
9.3 Expo growth decay comp.notebook
March 22, 2017
What percent of increase does each growth factor model?
TRY1
y=6(1.25)x
TRY2
y=2(1.4)x
TRY3
y=12(2.5)x
Jan 26­9:01 PM
9.3 Expo growth decay comp.notebook
March 22, 2017
What percent of decrease does each decay factor model?
TRY1
y=3(0.75)x
TRY2
y=4(0.4)x
TRY3
y=(0.135)x
Jan 26­9:01 PM
9.3 Expo growth decay comp.notebook
March 22, 2017
Compound Interest
A = balance after t years
P = principal or initial amount
r = annual interest rate as a decimal
n = number of times compounded per year
t = time in years
Ex.2
Write a compound interest equation to model a $1200 investment at a rate of 2% compounded quarterly.
How much money is there after three years?
TRY
Write a compound interest equation to model a $15,000 investment at a rate of 4.8% compounded monthly.
How much money is there after two years?
Jan 26­9:01 PM
9.3 Expo growth decay comp.notebook
March 22, 2017
Group Discussion
An exponential function models the amount of whole milk each person in the US drinks in a year. Graph the function y=21.5(0.955)x on your graphing calculator, where y is the number of gallons of whole milk and x is the number of years since 1975.
Make a table of values for the number of gallons consumed using values of x=0,5,10,15,20,25. Using your table and/or your grapher :
• Which x­value corresponds to the year 1995?
• In which year did the whole milk consumption fall to about 10.8gal/person?
• Use the function and your calculator to predict the whole milk consumption for the year 2010.
Jan 26­9:01 PM