Back to Graphing

Chapter 8.6

Exponential Functions

Principal Formula

General Growth Formula

• A = P (1 + r) t

• P = the original amount– sometimes called the principal

• r = rate of change

• t = time

Using General Growth Formula

• A = P (1 + r) t

• Deposit $475 into and interest-bearing account at 3.75%. How much will be in the account after two years?

• P is the deposit (principal).

• Rate is .0375 (converted from percentage)

• Time is 2 years.

• A = 475(1+.0375) 2

A = Find the Amount in the bank

• A = 475(1.0375) 2

• A = 475(1.07640625)

• A = 511.2929688

• In money, $511.29

A = P (1 + r) t

• According to 1991 records, 866 million people lived in the SE Asian country, India. At the time, it was growing at a rate of 1.9%. At this rate, what would be the population in 1996?

• P is the present population.• Rate is .019 (converted from percentage)• Time is 5 years.• A = 866(1+.019) 5

A = 866 million(1+.019) 5

• A = 866(1.019) 5

• A = 866(1.098679244)

• A = 951.4562254 million

• Approximately 951, 456, 000

Graphing Exponential Functions

How to Graph y =2x

• We can start with an x/y box.

• This is sort of a mathematical experiment.

• Follow these steps:

• We can then fill in some values for x.

• Insert the x-values into the equation to find y.

• Graph the (x,y) values

y =2x

y = 2 -2

y = 2 -1

y = 20 = 1

y = 22 = 4

y = 23 = 8

X Y

-2

-1

0

+1

+2

+3

1

4

1

2

y =2x

y = 2 -2

y = 2 -1

y = 20 = 1

y = 22 = 4

y = 23 = 8

X Y

-2

-1

0 1

+1 2

+2 4

+3 8

1

4

1

2

1

41

2

Graph the

results

(2, ¼)

(1, ½)

(0,1)

(1,2)

(2,4)

(3,8)

y =2x

Is it possible to

get a negative y

value?

ONLINE Graphing Calculator

• Can be found at this URL:

• http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

• OR CLICK HERE during the presentation.

Extra