A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
A population grows according to the logistic law with a limiting population of 5×109 individuals. The initial population of 109 begins growing by doubling every hour. What will the population be after 4 hours?
anonymous
 5 years ago
A population grows according to the logistic law with a limiting population of 5×109 individuals. The initial population of 109 begins growing by doubling every hour. What will the population be after 4 hours?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0109 should be \[10^9\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The equation I used was y' = r(1  (y/L))y The solution is y(t) = L / [1 + [(L/y0)  1] ]e^(rt) where y0 is y naught and represents the initial population. I initially solved for the rate using the DE. 2*(10^9) = r(1(10^9/5*10^9))10^9 I found r and then plugged and chugged with the solution. My answer was incorrect. Any ideas? How do I find the rate? I feel as if that is incorrect.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Haha you're making it much more difficult than it has to be. Try just doubling the initial value 4 times?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There is a limiting factor of 5*10^9 individuals, so that needs to be accounted for in the calculation. I have to use the equations above to calculate amount at t =4. I took the logistics law equation y' = r(1  (y/L))y and used that to find the rate. (r= rate, y= population, L = limiting factor) 2*(10^9) = r(1(10^9/5*10^9))10^9 I multiplied by 2 because the population initially doubled.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What do you get when you double 4x?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Then wouldn't it make sense that the population stops at 5e9? That's the property of the limit.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's carrying capacity. After a certain point, an ecosystem can't hold more individuals. At that point deaths or offspring decrease and growth stabilizes.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Meaning a plateau, right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the logistics equation needs to be used

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Alright, well then by definition the highest a population can get is the limiting factor. So, take the limit of the equation, and you'd get the 5e9, so that would be one way to use the equation to show that that is the highest it can get.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.