Exponential Growth and Decay. Linear GrowthExponential Growth Page 5

Exponential Growth and Decay

Linear Growth Exponential Growth

Annual Growth vs. Continuous Growth:

trPA )1(

Annual Growth:

timetraterprincipalPamountA

decimal) a (as (initial)

The +/- means you either add or subtract the rate depending upon the problem. Are you earning money or losing money?

02.000,15

? trPA )1( tA )02.1(15000 tA )02.1(15000

02.000,15

? trPA )1( tA )02.1(15000

tA )98(.15000

Here are the answers to the last two questions:

tA )02.1(15000 tA )98(.15000

This equation was an increasing problem. Notice that the number in the ( ) is greater than one!

This equation was a decreasing problem. Notice that the number in the ( ) is less than one!

Keep this in mind when doing annual growth problems!

trPA )1( tA )70(.10005)70(.1000A

07.168A

trPA )1( tA )05.1(50005)05.1(5000A5)05.1(5000A

407.6381A41.6381A

trPA )1( tA )12.1(18400

tA )88(.18400

420082012 t

4)88(.18400A

394.11034A

39.11034A

20 population Initial a)

%15 Rate b)

Before we do continuous growth, we need to look at the natural number “e”.

xey function Grpah the

This is very similar to the other exponential functions. “e” is called the natural number and is used to do continuous growth!

Annual Growth vs. Continuous Growth:

Continuous Growth:

principalP

amountA

decimal) a (as

(initial)

When we write the rate, we still need to change it to a decimal. If it is an increasing problem, we write the rate as a positive number. If it is a decreasing problem, then you write the rate as a negative number

02.000,15

Since this is an increasing problem, the rate is written as a positive.

Since this is a decreasing problem, the rate is written as a negative.

xexC 05.5000

505.50005 eC

127.64205 C

13.64205 C

xeA 0425.20000 60425.20000eA

232.25809A

23.25809A

xexf 00012101.100

100000012101.1001000 ef

60250993.881000 f

Exponential Growth and Decay. Linear GrowthExponential Growth Page 5

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