Exponential Growth and Decay. Linear GrowthExponential Growth Page 5.
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Exponential Growth and Decay
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Transcript of Exponential Growth and Decay. Linear GrowthExponential Growth Page 5.
Exponential Growth and Decay
Linear Growth Exponential Growth
Page 5
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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?
ttrPA
02.000,15
? trPA )1( tA )02.1(15000 tA )02.1(15000
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ttrPA
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!
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trPA )1( tA )70(.10005)70(.1000A
07.168A
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trPA )1( tA )05.1(50005)05.1(5000A5)05.1(5000A
407.6381A41.6381A
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trPA )1( tA )12.1(18400
tA )88(.18400
420082012 t
4)88(.18400A
394.11034A
39.11034A
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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:
rtPeA
timet
rater
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
ttrPA
02.000,15
?
Since this is an increasing problem, the rate is written as a positive.
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Since this is a decreasing problem, the rate is written as a negative.
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rtPeA
5
05.
5000
t
r
P
AA
xexC 05.5000
505.50005 eC
127.64205 C
13.64205 C
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rtPeA
6
0425.
20000
t
r
P
AA
xeA 0425.20000 60425.20000eA
232.25809A
23.25809A
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xexf 00012101.100
100000012101.1001000 ef
60250993.881000 f
