ALGEBRA 2/TRIG
Exponential Function:
Name:________________________________
Unit 6; 8.1-8.2: Exponential Growth and Decay
y  bx
b is the base – a positive number _________________________
x is an ________________________


Exponential Growth Functions: ____________________________
y  2x
x
y
***HA: ____________
2)
x
y  5x
y
***HA: ____________
End Behavior: _____________________________
Exponential Decay Functions: ____________________________
3)
y  2 x
x
y
***HA: ____________
4)
x
1
y
3
x
y
***HA:____________
End Behavior: _____________________________
*TRANSLATIONS to Exponential Growth and Decay Functions are similar to Parent Graph
Translations.
Translations
ALWAYS a HA at __________________________________
y = bx + k moves ___________ k units
y = bx – k moves ___________ k units
y = bx + h moves ___________ h units
y = bx – h moves ___________ h units
y = -bx
reflects over ________ axis
y = a * bx
5)
y  2 x1
vertical ______________________ or __________________________
movements: ______________________
HA:________________
6)
y  2 x 2  3
y  3  2 x 4
Y
movements: ______________________
HA:________________
7)
X
X
Y
movements: ______________________
______________________
*HA:_______________
X
Y
Exponential Growth:


y  a1  r 
Applications
t
When a quantity increases by a fixed percent each year (or another time period).
1+r is called the _______________________
1) In 1990, the cost of tuition at a state university was $4300. During the next 8 years, the tuition
rose 4% each year.
a) Write a model giving the tuition y (in dollars) t years after 1990.
b) Use the model to estimate the tuition in 2020.
2) In January, 1993, there were about 1.313 million Internet hosts. During the next five years, the
number of hosts increased by about 100% each year.
a) Write a model giving the number h (in millions) of hosts t years after 1993.
b) Use the model to estimate how many hosts there were in 1997.
Exponential Decay:


3)
y  a 1  r 
t
When a quantity decreases by a fixed percent each year (or another time period).
1–r is called the __________________________
You buy a new car for $24,000. The value y of the car decreases by 16% each year.
a) Write a model for the value of the car.
b) Use the model to estimate the value of the car after 2 years.
4)
There are 40,000 homes in your city. Each year 10% of the homes are expected to disconnect
from the septic system and connect to the sewer system.
a) Write a model representing the number of homes that still use septic systems.
b) Use the model to estimate the number of homes using septic systems after 5 years.
Compound Interest:
 r
A  P 1  
 n
nt
A = ____________________________________________
P = ____________________________________________
r = _____________________________________________
n = ____________________________________________
t = _____________________________________________
Annually:
Semiannually
Quarterly:
Weekly:
Monthly:
Daily:
n = ______
n = ______
n = ______
n = ______
n = ______
n = ______
5) You deposit $1500 into an account that pays 6% annual interest. Find the balance after 3 years if
the interest is compounded:
a) annually
b) quarterly
c) daily
6) You deposit $500 into an account that pays 3% annual interest. Find the balance after 2 years if
the interest is compounded:
b) monthly
b) weekly
c) daily