Please answer all parts in detail, thank you. Find the orthogonal trajectories of the family of...
6. Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 8000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years. (b) How long will it take for the population to increase to 4000?
(4 pts) Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation determine the constant k, and then solve the equation to find an expression for the size of the population after years. k= P(t) = (b) How long will it...
05.02. Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6900. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP/dt=kP(1−P/K), determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k=......................., P(t)=..................... (b) How long will it...
4. 1-/2 Points) PRACTICE ANOTHER DETAILS SCALCCC4 7.5.010.MI. MY NOTES Biologists stocked a lake with 200 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 14,000. The number of fish tripled in the first year, (a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the proutation after years. PC) (D) How long will it take for the population...
(1 point) Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 5500. The number of fish doubled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP dt - 2P (1-1) determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k= 0.7985...
Biologists stocked a lake with 300 fish and estimated the environmental carrying capacity to be 9700. The number of fish doubled in the first year. a. Assume that the size of the fish population satisfies the logistic equation ), where t is measured in years. = KP Find an expression for the size of the population. Hint: Use partial fraction decomposition to solve for P. P = b. How long will it take for the population to increase to 4850...
16. Find the orthogonal trajectories for the family of curves represented by 2x² + y2 = k, where k is a parameter.
Find the orthogonal trajectories of the family of curves. Use C for the constant. (I will "hand grade this one.) ka2 + y2 = 1
please answer all parts in detail thank u :) A random sample of 120 parts was taken from a big lot and was found that 111 of them met specification (a) [5 points] Construct a 99% confidence interval for population proportion p of parts that meet specification. (b) [5 points] Suppose that quality engineer wants to estimate the true proportion of parts that meet specification to within 0.04 with 95% confidence. How many parts should this quality engineer take? Assume...
Can you answer questions 2-6 please? Thanks This homework will be due on Wednesday Feb 19th in discussion. Question 1. A cell of some bacteria divides into two cells every 40 minutes. The initial population is 200 bacteria. Express the population after t minutes as a function of t. Question 2. Find the orthogonal trajectories of the family of curves y2 = 6cx. Question 3 Find the general solution of y" – 6y' +9y = 0 Question 4 Find the...