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4. 1-/2 Points) PRACTICE ANOTHER DETAILS SCALCCC4 7.5.010.MI. MY NOTES Biologists stocked a lake with 200...
6. Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population...
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...
(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...
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...
(1 point) Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal...
(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....
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...
2. [-75 Points] DETAILS SCALCCC4 7.5.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The population of...
2. [-75 Points] DETAILS SCALCCC4 7.5.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 100 billion. (Assume that the difference in birth and death rates is 20 million/year 0.02 billion/year.) (a) Write the logistic differential equation...
Please answer all parts in detail, thank you. Find the orthogonal trajectories of the family of...
Please answer all parts in detail, thank you.
Find the orthogonal trajectories of the family of curves y2 = kx5 Bilogists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish in that lake) to be 9000. The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after tyears.
1. [-/1 Points] DETAILS SCALCCC4 1.7.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the parametric...
1. [-/1 Points] DETAILS SCALCCC4 1.7.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the parametric equations below. x = 5t - 2 y = 3t + 1 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Eliminate the parameter to find a Cartesian equation of the...
4. [-16 Points] DETAILS SCALCCC4 3.4.090. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the tangent...
4. [-16 Points] DETAILS SCALCCC4 3.4.090. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the tangent equation to the given curve that passes through the point (10, 10). Note that due to the t2 in the x equation and the t3 in the y equation, the equation in the parameter t has more than one solution. This means that there is a second tangent equation to the given curve that passes through a different point. x = 6t2 + 4...
4. (-/1 Points] DETAILS SESSCALC2 4.1.012.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER When we estimate...
4. (-/1 Points] DETAILS SESSCALC2 4.1.012.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER When we estimate distances from velocity data, it is sometimes necessary to use times to, ti, tz, tz, ... that are not equally spaced. We can still estimate distances using the time periods At; = t; - t - 1. For example, a space shuttle was launched on a mission, the purpose of which was to install a new motor in a satellite. The table provided gives...
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...
(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...
2. [-75 Points] DETAILS SCALCCC4 7.5.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 100 billion. (Assume that the difference in birth and death rates is 20 million/year 0.02 billion/year.) (a) Write the logistic differential equation...
Please answer all parts in detail, thank you.
Find the orthogonal trajectories of the family of curves y2 = kx5 Bilogists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish in that lake) to be 9000. The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after tyears.
1. [-/1 Points] DETAILS SCALCCC4 1.7.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the parametric equations below. x = 5t - 2 y = 3t + 1 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Eliminate the parameter to find a Cartesian equation of the...
4. [-16 Points] DETAILS SCALCCC4 3.4.090. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the tangent equation to the given curve that passes through the point (10, 10). Note that due to the t2 in the x equation and the t3 in the y equation, the equation in the parameter t has more than one solution. This means that there is a second tangent equation to the given curve that passes through a different point. x = 6t2 + 4...
4. (-/1 Points] DETAILS SESSCALC2 4.1.012.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER When we estimate distances from velocity data, it is sometimes necessary to use times to, ti, tz, tz, ... that are not equally spaced. We can still estimate distances using the time periods At; = t; - t - 1. For example, a space shuttle was launched on a mission, the purpose of which was to install a new motor in a satellite. The table provided gives...
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