7.1 Exponential Models
Algebra H2
Name: ______________________________
ESSENTIAL UNDERSTANDING: Corresponding to every power, there is a root. The nth root of an
expression that contains an nth power as a factor can be simplified
Objectives: To model exponential growth and decay. To identify the growth/decay rate. To solve
problems involving exponential characteristics.
Key Terms: use your textbook to write out the definitions of these terms
General form of an exponential function:
Growth rate:
Decay rate:
Growth factor:
Decay factor:
Factor vs Rate: Find the rate of change for the given exponential functions
y = a(b)x
Growth/Decay
Factor = b
y = a(1 + r)x
Rate = r
y = 2(1.4)x
b = 0.97
1.3%
y = 0.3(1 – 0.5)x
y = 5(2)x
Modeling: Modeling an Exponential Situation
You buy a U.S. savings bond for $25. After one year, the bond is worth
$26.05. The second year, the bond is worth $27.14. Set up a chart of values.
Determine the growth factor and the growth rate per year. Write an
exponential function to model this situation. How much is the bond worth
after fifteen years? Fifty years?
x
0
1
2
y
25
26.05
27.14
How do you determine the growth rate or decay rate for an exponential function given consecutive output
values?
Modeling: Annual Interest Rate
You open a savings account that pays 4.5% annual interest. You initially invest $300 and you make no
additional deposits or withdrawals. Write an equation to model this situation. How many years will it
take for the account to grow to at least $500?
When is an exponential function an appropriate model?
Modeling: Compound Interest Rate
An MIHS student’s parents invest $10, 000 in an account that pays 8.5% interest per year, compounded
quarterly when she is born. What was the amount of money in the
account after 3 years? When she graduates from MIHS?
P = C (1 + r/n) nt where
P = future value
C = initial deposit
r = interest rate
n = # of times per year interest in compounded
t = number of years invested
Modeling: Writing an Exponential Function
A music store sold 200 guitars in 2007. The store sold 180 guitars in 2008. The number of guitars that the
store sells is decreasing exponentially. If this trend continues, how many guitars will the store sell in 2012?
Got it? Suppose you invest $500 in a savings account that pays 3.5% annual interest. How much will be
in the account after five years? When will the account contain at least $650?
Got it? The population of Bainsville is 2000. The population is supposed to grow by 10% each year for the
next 5 years. How many people will live in Bainsville in 5 years?
Got it? How much money should I save in an account paying 5% interest compounded monthly if I want to
have $6000 in 6 months?