12x1 t04 02 growth & decay (2011)
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TRANSCRIPT
![Page 1: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/1.jpg)
Exponential Growth & Decay
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Exponential Growth & DecayGrowth and decay is proportional to population.
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Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
![Page 4: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/4.jpg)
Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
kPdPdt 1
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Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
PdP
kt 1
kPdPdt 1
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Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
PdP
kt 1
cPk
log1
kPdPdt 1
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Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
PdP
kt 1
cPk
log1
cPkt log
kPdPdt 1
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Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
PdP
kt 1
cPk
log1
cPkt logcktP log
kPdPdt 1
![Page 9: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/9.jpg)
Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
PdP
kt 1
cPk
log1
cPkt logcktP log
ckteP
kPdPdt 1
![Page 10: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/10.jpg)
Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
PdP
kt 1
cPk
log1
cPkt logcktP log
ckteP ckt eeP
kPdPdt 1
![Page 11: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/11.jpg)
Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
PdP
kt 1
cPk
log1
cPkt logcktP log
ckteP ckt eeP
ktAeP
kPdPdt 1
![Page 12: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/12.jpg)
Exponential Growth & Decay
kPdtdP
Growth and decay is proportional to population.
PdP
kt 1
cPk
log1
cPkt logcktP log
ckteP ckt eeP
ktAeP
P = population at time t
A = initial population
k = growth(or decay) constantt = time
kPdPdt 1
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e.g.(i) The growth rate per hour of a population of bacteria is 10% of the population. The initial population is 1000000
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e.g.(i) The growth rate per hour of a population of bacteria is 10% of the population. The initial population is 1000000
equation. aldifferenti theosolution t a is that Show a) 1.0 tAeP
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e.g.(i) The growth rate per hour of a population of bacteria is 10% of the population. The initial population is 1000000
equation. aldifferenti theosolution t a is that Show a) 1.0 tAeP tAeP 1.0
![Page 16: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/16.jpg)
e.g.(i) The growth rate per hour of a population of bacteria is 10% of the population. The initial population is 1000000
equation. aldifferenti theosolution t a is that Show a) 1.0 tAeP tAeP 1.0
tAedtdP 1.01.0
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e.g.(i) The growth rate per hour of a population of bacteria is 10% of the population. The initial population is 1000000
equation. aldifferenti theosolution t a is that Show a) 1.0 tAeP tAeP 1.0
tAedtdP 1.01.0
P1.0
![Page 18: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/18.jpg)
e.g.(i) The growth rate per hour of a population of bacteria is 10% of the population. The initial population is 1000000
equation. aldifferenti theosolution t a is that Show a) 1.0 tAeP tAeP 1.0
figures.t significan 4 correct to hours213after population theDetermine b)
tAedtdP 1.01.0
P1.0
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e.g.(i) The growth rate per hour of a population of bacteria is 10% of the population. The initial population is 1000000
equation. aldifferenti theosolution t a is that Show a) 1.0 tAeP tAeP 1.0
figures.t significan 4 correct to hours213after population theDetermine b)
tePA
Pt
1.010000000000001
1000000,0when
tAedtdP 1.01.0
P1.0
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e.g.(i) The growth rate per hour of a population of bacteria is 10% of the population. The initial population is 1000000
equation. aldifferenti theosolution t a is that Show a) 1.0 tAeP tAeP 1.0
figures.t significan 4 correct to hours213after population theDetermine b)
tePA
Pt
1.010000000000001
1000000,0when
tAedtdP 1.01.0
P1.0
0001941 1000000,5.3when 5.31.0
ePt
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e.g.(i) The growth rate per hour of a population of bacteria is 10% of the population. The initial population is 1000000
equation. aldifferenti theosolution t a is that Show a) 1.0 tAeP tAeP 1.0
figures.t significan 4 correct to hours213after population theDetermine b)
tePA
Pt
1.010000000000001
1000000,0when
bacteria 1419000 is therehours213after
tAedtdP 1.01.0
P1.0
0001941 1000000,5.3when 5.31.0
ePt
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(ii) On an island, the population in 1960 was 1732 and in 1970 it was 1260.
a) Find the annual growth rate to the nearest %, assuming it is proportional to population.
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(ii) On an island, the population in 1960 was 1732 and in 1970 it was 1260.
a) Find the annual growth rate to the nearest %, assuming it is proportional to population.
kPdtdP
![Page 24: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/24.jpg)
(ii) On an island, the population in 1960 was 1732 and in 1970 it was 1260.
a) Find the annual growth rate to the nearest %, assuming it is proportional to population.
kPdtdP
ktAeP
![Page 25: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/25.jpg)
(ii) On an island, the population in 1960 was 1732 and in 1970 it was 1260.
a) Find the annual growth rate to the nearest %, assuming it is proportional to population.
kPdtdP
ktAeP
ktePA
Pt
17321732
1732,0when
![Page 26: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/26.jpg)
(ii) On an island, the population in 1960 was 1732 and in 1970 it was 1260.
a) Find the annual growth rate to the nearest %, assuming it is proportional to population.
kPdtdP
ktAeP
ktePA
Pt
17321732
1732,0when
kePt
1017321260i.e.1260,10when
![Page 27: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/27.jpg)
(ii) On an island, the population in 1960 was 1732 and in 1970 it was 1260.
a) Find the annual growth rate to the nearest %, assuming it is proportional to population.
kPdtdP
ktAeP
ktePA
Pt
17321732
1732,0when
kePt
1017321260i.e.1260,10when
1732126010 ke
![Page 28: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/28.jpg)
(ii) On an island, the population in 1960 was 1732 and in 1970 it was 1260.
a) Find the annual growth rate to the nearest %, assuming it is proportional to population.
kPdtdP
ktAeP
ktePA
Pt
17321732
1732,0when
kePt
1017321260i.e.1260,10when
1732126010 ke
17321260log
101
17321260log10
k
k
![Page 29: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/29.jpg)
(ii) On an island, the population in 1960 was 1732 and in 1970 it was 1260.
a) Find the annual growth rate to the nearest %, assuming it is proportional to population.
kPdtdP
ktAeP
ktePA
Pt
17321732
1732,0when
kePt
1017321260i.e.1260,10when
1732126010 ke
17321260log
101
17321260log10
k
k
0318165.0k
![Page 30: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/30.jpg)
(ii) On an island, the population in 1960 was 1732 and in 1970 it was 1260.
a) Find the annual growth rate to the nearest %, assuming it is proportional to population.
kPdtdP
ktAeP
ktePA
Pt
17321732
1732,0when
kePt
1017321260i.e.1260,10when
1732126010 ke
17321260log
101
17321260log10
k
k
0318165.0k
3%-isrategrowth
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b) In how many years will the population be half that in 1960?
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b) In how many years will the population be half that in 1960?kteP 1732866 ,866when
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b) In how many years will the population be half that in 1960?kteP 1732866 ,866when
21log1
21log
21
kt
kt
ekt
![Page 34: 12X1 T04 02 growth & decay (2011)](https://reader034.vdocuments.net/reader034/viewer/2022042813/548964f3b479590a0d8b595c/html5/thumbnails/34.jpg)
b) In how many years will the population be half that in 1960?kteP 1732866 ,866when
21log1
21log
21
kt
kt
ekt
786.21t
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b) In how many years will the population be half that in 1960?kteP 1732866 ,866when
21log1
21log
21
kt
kt
ekt
786.21thalved haspopulationtheyears 22In
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Exercise 7G; 2, 3, 7, 9, 11, 12
b) In how many years will the population be half that in 1960?kteP 1732866 ,866when
21log1
21log
21
kt
kt
ekt
786.21thalved haspopulationtheyears 22In