The population of a particular type of fish in a lake would grow logistically according to the differential equation (where t is measured in years) absent harvesting.\\ $\frac{dy}{dt} = 0.08y(1 - \frac{y}{2600})$\ y(0) = 1080\ If this lake is opening to fishing, determine how many fish can be harvested each year to maintain the population in equilibrium.\ \\ fish per year\ Give your answer to the nearest whole fish
Added by Iker C.
Close
Step 1
The differential equation becomes: $\frac{dy}{dt} = 0.08y(1 - \frac{y}{2600}) - h$ In equilibrium, $\frac{dy}{dt} = 0$. Therefore, $0.08y(1 - \frac{y}{2600}) - h = 0$ $0.08y - \frac{0.08y^2}{2600} - h = 0$ $\frac{0.08y^2}{2600} - 0.08y + h = 0$ $0.08y^2 - 208y + Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 57 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The population of a particular type of fish in a lake would grow logistically according to the differential equation (where t is measured in years) absent harvesting: dy/dt = 0.08y(1 - y/1500) y(0) = 210 If this lake is opening to fishing, determine how many fish can be harvested each year to maintain the population in equilibrium. fish per year Give your answer to the nearest whole fish.
Sri K.
The population of a particular type of fish in a lake would grow logistically according to the differential equation (where t is measured in years) absent harvesting: dy / dt = 0.03y (1 - y / 4000) y(0) = 570 If this lake is opening to fishing, determine how many fish can be harvested each year to maintain the population in equilibrium. fish per year
Madhur L.
(1 point) A pond of fish starts with 280 fish: The pond can sustain 520 fish, 1 fish die each year while the number of births is 50% of the current population: 2.19699E+07 fish are harvested from the pond each year: Write a differential equation that models the problem. What is the long-term population of the fish?
Suman K.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD