s-shaped growth
DESCRIPTION
S-shaped growth. Flowers. Logistic Equation. dA / dt = r * A * (K-A) / K. r net growth rate for non-stressed growth K carrying capacity Ao initial population (or Area). If ATRANSCRIPT
![Page 1: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/1.jpg)
S-shaped growth
Flowers
![Page 2: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/2.jpg)
dA / dt = r * A * (K-A) / K
If A<<K then (K-A) / K ~1And we have exponential growth
Logistic Equation
r net growth rate for non-stressed growthK carrying capacityAo initial population (or Area)
![Page 3: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/3.jpg)
dA / dt = r * A * (K-A) / K = r*A - r*A*(A/K)
If A<<K then (K-A) / K ~1And we have exponential growth
![Page 4: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/4.jpg)
r net growth rate for non-stressed growthK carrying capacityAo – initial population (or Area)
![Page 5: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/5.jpg)
![Page 6: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/6.jpg)
![Page 7: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/7.jpg)
S-shaped growth
FlowersVerifys
![Page 8: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/8.jpg)
Problems with Logistic Equation
• Simple One example of s-shaped growth• The linear decrease in growth rate is often not
true in real life.• The logistic equation fails to highlight the
mechanisms responsible for limited growth. i.e. is it a decrease in birth rate or an increase in death rate.
![Page 10: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/10.jpg)
A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-
zero levelD. S-shaped growth
![Page 11: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/11.jpg)
A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-
zero levelD. S-shaped growth
![Page 12: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/12.jpg)
A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-
zero levelD. S-shaped growth
![Page 13: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/13.jpg)
A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-
zero levelD. S-shaped growth
![Page 14: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/14.jpg)
A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-
zero levelD. S-shaped growth
Growth rate=rate*(1-stock/100)
![Page 15: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/15.jpg)
A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-
zero levelD. S-shaped growth
Growth rate=rate*(1-stock/100)
![Page 16: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/16.jpg)
A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-
zero levelD. S-shaped growth
![Page 17: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/17.jpg)
A. Exponential growthB. Exponential decay (goal seeking) to zeroC. Exponential decay (goal seeking) to a non-
zero levelD. S-shaped growth
![Page 18: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/18.jpg)
The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80?
A. Series 1B. Series 2C. Series 3D. Series 4
![Page 19: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/19.jpg)
The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80?
A. Series 1B. Series 2C. Series 3D. Series 4
![Page 20: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/20.jpg)
A. Series 1B. Series 2C. Series 3D. Series 4
The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80 and an intrinsic growth rate of 5 %?
![Page 21: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/21.jpg)
A. Series 1B. Series 2C. Series 3D. Series 4
The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80 and an intrinsic growth rate of 5 %?
![Page 22: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/22.jpg)
The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 100 and an initial value of 4?
A. Series 1B. Series 2C. Series 3D. Series 4
![Page 23: S-shaped growth](https://reader035.vdocument.in/reader035/viewer/2022062221/56814420550346895db0bda1/html5/thumbnails/23.jpg)
The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 100 and an initial value of 4?
A. Series 1B. Series 2C. Series 3D. Series 4