Sect. 5.2
Exponential Function: function in the form of y = abx where a≠0 and b is a positive number other than 1.
General Form: y = abx­h + k
Exp. Growth Function: when a>0 and b>1.
Exp. Decay Function: when a >0 and 0<b<1.
asymptote: a line that a graph approaches more and more closely.
Ex. 1
Graph f(x) = 3x; state the domain, range, and asymptote.
y
6
5
4
3
2
1
­6
­5
­4
­3
­2
­1
0
­1
­2
­3
­4
­5
­6
x
1
2
3
4
5
6
Ex. 2
Graph f(x) = State the domain, range, and asymptote.
Observe the following graphs of exponential functions and look for patterns in them.
Ex. 3
Describe how to graph the following from the graph of f(x) = 2x.
a. g(x) = 2x­3
b. h(x) = 2x­ 4
c. k(x) = 5­0.5x
Exponential Growth
Formula
y = a(1+r)t
Exponential Decay
Formula
y = a(1­r)t
a = initial amount
r = rate
t = time
1+r = growth factor
1­r = decay factor
Ex. 4
In the last 12 years, the population of buffalo in a state park has grown by about 7% per year. If the initial amount was 38 buffalo, how many were there in 11 years?
After how many years were there 53 buffalo?
Ex. 5
College tuition at a local school is $8300. If it increases at a rate of 4% annual interest each year, what will be the cost in 5 years?
Ex. 6
A new Honda Civic costs $28,000. It depreciates at a rate of 16% each year. Find the value after 2 years.
After how many years would the value drop to $12,000?
Compounded Interest
A =
P = principal (deposit)
r = rate
n = # of times compounded
t = time Ex. 7 Suppose $100,000 is invested at 6.5% interest, compounded semiannually. Find the amount in the account at t = 0, 4, 8, and 10 years. When will the amount reach $400,000?
The natural base e:
As n ∞, (1 + 1/n)n e≈2.71828... (irrational #)
Calculate each value to four decimal places:
a) e3
b) e­0.23
c) e0
y
Ex. 8
Graph f(x) = ex
6
5
4
3
2
1
­6
­5
­4
­3
­2
­1
0
­1
­2
­3
­4
­5
­6
x
1
2
3
4
5
6
Ex. 9
Describe the transformation of the following from the graph of f(x) = ex:
a) g(x) = ex+3
b) h(x) = e­0.5x
c) k(x) = 1 ­ e­2x