Algebra 1 Common Core Student Edition, Grade 8-9

Ex p o n e n t i a l Gr o w t h

and Decay

Objective To m odel exponential growth a n d decay

Common Core State Standards

F-IF.C.8b Use the properties of exponents to

interpret expressions for exponential fu n ctio n s...

A ls o A-SSE.B.3C, A -C E D .A .2 , F-LE.A.1c, F-LE.B.5

M P 1, M P 2, M P 3, M P 4, M P 8

" ' Getting Ready! « x C

Uranium-238

The h alf - lif e of a radioact ive subst ance is t he length

of time it takes for half of the atoms in a sample of

the substance to decay. The half-life of uranium-238

is 4.46 x 109 yr.

Su p p o se y o u h av e a sam p l e o f 1 0 0 0 u r a n i u m - 2 3 8

at om s. How many at om s of uranium -238 ar e l ef t af t er

1.338 x 1010 yr? Explain your reasoning.

Try a simpler

problem. How many

atoms are le ft a fte r

4.46 x 109 years?

Will the result

fo r 1.338 x 1010

be g re a te r or less

than th e re su lt fo r

4 .4 6 x 109 y e a rs? .......................................................

mathematical In th e Solve It, the n u m b e r of uranium -238 atom s decreases exponentially. In this

PRACTICES lesson, you will use exponential functions to m odel sim ilar situations.

Essent ial Und er st and ing An exponential function can m odel growth or decay

of an initial amount.

Lesson

Vocabulary

exponential

growth

growth factor

compound

interest

exponential

decay

decay factor

Key Concep t Exponential Growth

Definitions

Exponential grow th can be m odeled by th e function

y= a • bx, where a > 0 and b > 1. The base b is the

growth factor, w hich equals 1 plus the p ercen t rate of

change expressed as a decim al.

Graph

Algebra

in itial a m o u n t (w hen x = 0)

exponent

I

abx

t

The base, w hich is g re a te r

th a n 1, is th e grow th factor.

460 Ch ap t er 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

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