7-7 Exponent ial Growt h and Decay
Quick Review
When a > 0 and b > 1, th e function y = a • b* m odels
exponential growth. The base b is called th e growth
factor. When a > 0 and 0 < b < 1, th e function
y = a • b* m odels exponential decay. In this case the
base b is called th e decay factor.Example
The population of a city is 25,000 and decreases 1% each
year. Predict the population after 6 yr.y = 25,000 • 0.99* Exponential decay function
= 25,000 • 0.996 Substitute 6 for x.
~ 23,537 Simplify.The population will be ab o u t 23,537 after 6 yr.Exercises
Tell whether the function represents exponential growth
or exponential decay. Identify the growth or decay factor.- y = 5.2 • 3X 73. / ( x ) = 7 • 0.32*
74.y=0.15(|)X 75. g(x) = 1.3( | ) x- Finance Suppose $2000 is d ep o sited in an account
paying 2.5% interest c o m p o u n d ed quarterly. W hat
will th e acco u n t balance be after 12 yr? - Music A b a n d perform s a free concert in a local
park. There are 200 p eople in th e crowd at th e start
of th e concert. The n u m b e r of people in th e crowd
grows 15% every h alf hour. How m any p eople are in
th e crowd after 3 h? R ound to th e n ea rest person.
7-8 Geomet ric Sequences
Quick Review
In a geom etric sequence th e ratio of any term to its
preceding term is a co n stan t value.Example
Find the common ratio of the geometric sequence.
2, 6 , 1 8 , 5 4 ,...X 3 X 3 X 3
The com m on ratio of th e geom etric sequence is 3.
Write a recursive formula to represent the geometric
sequence.
256, 64, 16, 4 ,...Exercises
Find the common ratio of each geometric sequence.- 10, 20, 40, 8 0 ,...
- 1,10,100,1000,...
- 100, 20, 4, 0. 8 ,. ..
- 6561,2187, 729, 2 4 3 ,...
Write a recursive formula to represent the geometric
sequence.- 20, 60,180, 5 4 0 ,...
- 5, 2.5, 1.25, 0 .6 2 5 ,...
- 3, 12, 48,192,...
- 10,1,0.1,0.01,...
478 Ch ap t er 7 Ch ap t er Revi ew