Section 4-1
1
Math 150 Lecture Notes
Exponential Functions
The exponential function with base a is defined for all real numbers x by f(x) = a
x
where a > 0 and
a ≠ 1.
The exponential function f(x) = a
x
(a > 0, a ≠ 1) has domain (-∞, ∞) and range (0, ∞).
The line y = 0 (the x-axis) is a horizontal asymptote of f. The graph of f has one of the following
shapes.
The natural exponential function is the exponential function f(x) = e
x
with base e. It is often
referred to as the exponential function.
Compound interest is calculated by the formula
nt
n
r
PtA
+= 1)( where
A(t) = amount after t years
P = principal
r = interest rate per year
n = number of times interest is compounded per year
t = number of years
Continuously compounded interest
is calculated by the formula A(t) = Pe
rt
where
A(t) = amount after t years
P = principal
r = interest rate per year
t = number of years
Example 1: Use a calculator to evaluate the function f(x) = (¾)
2x
at the values f(0.7), f( 7 /2),
f(1/π), f(2/3). Round your answer to three decimal places.
