Algebra 1 Common Core Student Edition, Grade 8-9

How can you ident ify
a co n st an t r at io
between y-values?
When you mul t i pl y each
y- value by t he same
const ant and get t he
next y-value, there is a
constant ratio between
the values.

Why is t he function

30 • 2X not 2 • 30x?

In an exponent i al

function, a is the starting

value and b is the

common rat io.

Suppose all the x-values in a table have a common difference. If all the y-values have a

common difference, then the table represents a linear function. If all of the y-values have

a common ratio, then the table represents an exponential function.

Id ent ifying Lin ear and Exp o nent ial Functions

Does the table or rule represent a linear or an exponential function? Explain.

0

-+ 1 +1 +1

8 0

1 2 3

O-i -3 -9 -27

Th e d i f f eren ce

between each

x- value is 1. 012

-1 -3 -9

x 3 x 3 x 3

Th e r at i o b et w een

each y- valu e is 3.

The table represents an exponential function. There is a common difference between

x-values and a common ratio between y-values.

0y = 3x

The rule represents a linear function. The independent variable x is not an exponent.

vJ|Gotlt? 1. Does the table or rule represent a linear or an exponential function?

Explain.

a. b. y = 3 • 6 X

II 41 2 3

-1 1 3

^BS2B5BEv a l u a t i n g a n Ex p o n e n t i a l Fu n ct i o n j j f R I D D E D RESPO N SE

Po p u l at i o n Gr o w t h Suppose 30 flour beetles are left undisturbed in a warehouse

bin. The beetle population doubles each week. The function / ( x ) = 30 • 2X gives the

population after x weeks. How many beetles will there be after 56 days?

f{x) = 30 • 2X

= 30 • 2s 56 days is equal to 8 weeks. Evaluate the function for x = 8.

= 30 • 256 Si m p l i f y t h e p o w er.

= 7680 Si m p l i f y.

After 56 days, there will be 7680 beetles.

Go t It? 2. An initial population of 20 rabbits triples every half year. The function

fix) = 20 • 3A gives the population after x half-year periods. How many

rabbits will there be after 3 yr?

454 Chapter 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s