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Mathematics LibreTexts

18.8: Growth Models

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1.

  1. P0=20.Pn=Pn1+5
  2. Pn=20+5n

3.

  1. P1=P0+15=40+15=55.P2=55+15=70
  2. Pn=40+15n
  3. P10=40+15(10)=190 thousand dollars
  4. 40+15n=100 when n=4 years.

5. Grew 64 in 8 weeks: 8 per week

  1. Pn=3+8n
  2. 187=3+8n.n=23 weeks

7.

  1. P0=200 (thousand), Pn=(1+.09)Pn1 where n is years after 2000
  2. Pn=200(1.09)n
  3. P16=200(1.09)16=794.061( thousand )=794,061
  4. 200(1.09)n=400.n=log(2)/log(1.09)=8.043. In 2008

9. Let n=0 be 1983.Pn=1700(2.9)n.2005 is n=22.P22=1700(2.9)22=25,304,914,552,324 people. Clearly not realistic, but mathematically accurate.

11. If n is in hours, better to start with the explicit form. P0=300.P4=500=300(1+r)4

500/300=(1+r)4.1+r=1.136.r=0.136

  1. P0=300.Pn=(1.136)Pn1
  2. Pn=300(1.136)n
  3. P24=300(1.136)24=6400 bacteria
  4. 300(1.136)n=900.n=log(3)/log(1.136)= about 8.62 hours

13.

  1. P0=100Pn=Pn1+0.70(1Pn1/2000)Pn1
  2. P1=100+0.70(1100/2000)(100)=166.5
  3. P2=166.5+0.70(1166.5/2000)(166.5)=273.3

15. To find the growth rate, suppose n=0 was 1968. Then P0 would be 1.60 and P8=2.30=1.60(1+r)8,r=0.0464. since we want n=0 to correspond to 1960 , then we don't know P0, but P8 would 1.60=P0(1.0464)8. P0=1.113

  1. Pn=1.113(1.0464)n
  2. P0=$1.113, or about $1.11
  3. 1996 would be n=36.P36=1.113(1.0464)36=$5.697. Actual is slightly lower.

17. The population in the town was 4000 in 2005, and is growing by 4% per year.


This page titled 18.8: Growth Models is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform.

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