Related Rates
Unlock all 21 questions & worked solutions
You're viewing a free preview. Create an account to access the complete question set, step-by-step solutions, and progress tracking.
All Questions
Access the full question set for every topic.
Worked Solutions
Step-by-step explanations for every answer.
Track Progress
Mark questions right or wrong and monitor your growth.
It's Free
No credit card required - sign up in under a minute.
The carrying capacity to the hectare for a population \(P\) of a flock of sheep is calculated to be 100 sheep to the hectare. The logistic differential equation for \(P\) is given by
\[\frac{dP}{dt} = 0.01 P(100-P) \text{ at time } t \text{ years.}\]
(i) Show that \(P = \frac{100}{1+Ke^{-t}}\) is a solution to the logistic differential equation.
(ii) If initially \(P=10\), find \(K\) and hence the population when \(t = 5\).
📚 Want More Questions?
There are 20 more questions available. Create your free account to access the complete question set with detailed solutions.