Algebra 1 Common Core Student Edition, Grade 8-9

Is th e fo r m u la an
exponential growth
function?
Yes. You can r e w rite
th e fo rm u la as
■a-PKi+Sn'.
So it is an e xp o n en tia l
function w ith initial
amount P and growth
factor (1 +fj)n.

You can use th e following form ula to find the balance of an acco u n t th a t earns

c o m p o u n d interest.

A = p [ l + Ji)nt A = th e b alance

P = th e principal (the initial deposit)

r = th e an n u a l in tere st rate (expressed as a decim al)

n = th e n u m b e r of tim es interest is c o m p o u n d ed p er year

t = th e tim e in years

Problem 2 Co m p o u n d I n t er e st

Finance Suppose that when your friend was born, your friend's parents deposited

$2000 in an account paying 4.5% interest compounded quarterly. What will the

account balance be after 18 yr?

Know ,

• $2000 principal


• 4.5% interest
  
  
  • interest compounded quarterly
  
  
  
  

A = H 1 + Tdnt

= 2000^1 + (L M ij418

A cc o u n t balance in 18 yr

Use the com pound interest form ula.

Substitute the values for P, r , n , a n d t.

Simplify.

Use th e co m p o u n d

interest form ula.

= 2000(1.01125)72

The balance will be $4475.53 after 18 yr.

& G ot It? 2. Suppose th e account in Problem 2 pays interest c o m p o u n d ed m onthly.

W hat will th e account balance be after 18 yr?

The function y = a • bx can m odel exponential decay as well as exponential growth.

In both cases, b is d eterm in e d by th e p ercen t rate of change. The value of b tells if the

equation m odels exponential growth or decay.

Key Concept Exponential Decay

Definitions

Exponential decay can be m od eled by th e function

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

decay factor, w hich equals 1 m inus th e p ercen t rate of

change expressed as a decim al.

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

y _ aa • bx. exponent

t

The base is the decay factor.

462 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