1. GROWTH factor Exponential Growth An exponential function, ,
can be used to model growth when b > 1.
When b > 1, b is the ____________________________.
Exponential Growth Example
1. Since 1985, the daily cost of patient care in community hospitals in the US has increased about 8.1% per year. In 1985, such hospital costs were an average of $460 per day. Write an equation to model the cost of hospital care and find the approximate cost per day in 2000.
HINT! Define all of your variables FIRST!
y (dependent variable) is what you are modeling y =
a is the starting amount (when x = 0) a =
b is the growth factor (100% plus the percent of increase) b =
changed into decimal form
x (independent variable) often represents the time factor x =
You will see growth in a positive direction
when a is greater than zero
and b is greater than 1.
GROWTH factor
You will see growth in a negative direction
when a is less than zero
and b is greater than 1.

2. DECAY factor Exponential Decay An exponential function, ,
can be used to model growth when 0 < b < 1.
When b < 1, b is the ____________________________.
Exponential Decay Example
2. In 1990, the population of Washington, D.C., was about 604,000 people. Since then the population has decreased about 1.8% per year. If the trend continues, predict what the population of Washington, D.C., will
be in 2010 (before the Census tells us exactly).
HINT! Define all of your variables FIRST!
y (dependent variable) is what you are modeling y =
a is the starting amount (when x = 0) a =
b is the decay factor (100% minus the percent of decrease) b =
changed into decimal form
x (independent variable) often represents the time factor x =
You will see decay from a positive realm
when a is greater than zero
and b is less than 1.
DECAY factor
You will see decay from a negative realm
when a is less than zero
and b is greater than 1.