

Course 1, Unit 5  Exponential Functions
Overview
In the Exponential Functions unit, students analyze situations
that can be modeled well by rules of the form y = a(b)^{x}.
They construct and use data tables, graphs, and equations in the form y = a(b)^{x} to
describe and solve problems about exponential relationships such as population
growth, investment of money, and decay of medicines and radioactive materials.
Some of these topics are often introduced in middle school math courses.
Encourage your student to recall these ideas. Some of these questions may
be helpful. They also use exponent rules to simplify exponential and
radical expressions.
Key Ideas from Course 1, Unit 5

Exponential growth or decay relationship: In the rule y = a(b)^{x}, b is
the constant growth or decay factor. In tables where x is
increasing in uniform steps, the ratios of succeeding y values
will always be b. If b is greater than 1, the pattern
will be exponential growth; if b is between 0 and 1, the pattern
will be exponential decay. The value of a indicates the yintercept
(0, a) of the graph of the relationship.
For example, y = 4(0.5)^{x} represents
an exponential decay relationship between x and y,
where the initial value of y (when x = 0)
is 4, and the y values decrease by 50% for each increase of
1 in x values. The table would begin as follows:

NOWNEXT equations: Since exponential growth involves
repeated multiplication by a constant factor, those patterns can
be represented by equations in the general form NEXT = b * NOW, starting
at a. For example, the pattern of change in a population growing
at a rate of 20% per year from a base of 5 million in the year
2000 can be expressed as NEXT = 1.20NOW, starting
at 5. (See pages 291301.)
Year 
2000

2001

2002

2003

Population
(in millions) 
5

6

7.2

8.64


Rewriting exponential expressions: See the unit summary below
for the exponent rules. Practice using these rules is distributed
throughout the Review tasks in subsequent units. (See pages 304306,
332337.)
Example:
