Answer:
it is the second one
Step-by-step explanation:
Answer:
![\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%202.4P%281%20-%20%5Cfrac%7BP%7D%7B1200%7D%29)
Step-by-step explanation:
The logistic differential equation is as follows:
![\frac{dP}{dt} = rP(1 - \frac{P}{K})](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%20rP%281%20-%20%5Cfrac%7BP%7D%7BK%7D%29)
In this problem, we have that:
, which is the carring capacity of the population, that is, the maximum number of people allowed on the beach.
At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour.
This means that
when
. With this, we can find r, that is, the growth rate,
So
![\frac{dP}{dt} = rP(1 - \frac{P}{K})](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%20rP%281%20-%20%5Cfrac%7BP%7D%7BK%7D%29)
![400 = 200r(1 - \frac{200}{1200})](https://tex.z-dn.net/?f=400%20%3D%20200r%281%20-%20%5Cfrac%7B200%7D%7B1200%7D%29)
![166.67r = 400](https://tex.z-dn.net/?f=166.67r%20%3D%20400)
![r = 2.4](https://tex.z-dn.net/?f=r%20%3D%202.4)
So the differential equation is:
![\frac{dP}{dt} = rP(1 - \frac{P}{K})](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%20rP%281%20-%20%5Cfrac%7BP%7D%7BK%7D%29)
![\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%202.4P%281%20-%20%5Cfrac%7BP%7D%7B1200%7D%29)
1. 13*13*13 =2197
2. 2/5*2/5 = 4/25
3. 0.9*0.9 = 0.81
Answer:
The correct answer for this problem is the 2nd one because all you have to do is count how far each one is from -1 and -2
Step-by-step explanation: