Harvesting Fish. A fish farmer has 5000 catfish in a pond. The number of catfish increases...

Harvesting Fish. A fish farmer has 5000 catfish in a pond. The number of catfish increases by 8% per month and the farmer harvests 420 catfish per month.

a) (4 points) Find a recursive equation for the catfish population Pn for each month.

b) (4 points) Solve the recursive equation to find an explicit equation for the catfish population.

c) (3 points) How many catfish are in the pond after six months?

d) (3 points) Is harvesting 420 catfish per month a sustainable strategy for the fish farmer?

e) (4 points) What is the maximum number of catfish the fish farmer can harvest to sustain his business?

Solutions

Expert Solution

Colby Messinger answered 1 month ago

Next > < Previous

Related Solutions

The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish,...

The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows. Catfish Bass Bluegill Pike 121 76 237 66 In the 5-year interval, did the distribution of fish change at the 0.05 level? (a) What is the level of...

A water harvesting pond is to be constructed by constructing an embankment across a narrow valley....

A water harvesting pond is to be constructed by constructing an embankment across a narrow valley. The top width of the embankment is kept at 3.6 m. using the information in the Table Q8, and taking the upstream and downstream side slopes as 3:1 and 2:1 respectively, a settlement allowance of 12.5%: . Fill up the table and estimate the earth volume required to construct the dam. Show sample calculations only. . Sketch the plan view, longitudinal section and centre...

Researchers used a standard fish seine to sample the fish population of Mason Pond. Most of...

Researchers used a standard fish seine to sample the fish population of Mason Pond. Most of these fish were bluegill (Lepomis macrochirus). Researchers removed fish from the seine and measured these fish on a fish board the boat. Researchers measured each fish to the nearest millimeter. Then, researchers measured all of the fish brought in by your seine, except for fish less than 15 mm. Size Category Observed Expected 15-35 mm 22 7.33 >35-55 mm 16 5.33 >55 mm...

Assume there is a certain population of fish in a pond whose growth is described by...

Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1000 fish. Absent constraints, the population would grow by 240% per year. If the starting population is given by p 0 = 600 , then after one breeding season the population of the pond is given by p 1 = After two breeding seasons the population of the pond is...

suppose a manager of yalelo is observing the fish pond to determine when it will be...

suppose a manager of yalelo is observing the fish pond to determine when it will be ready for sale. let x represent the length of a single bream taken at random from the pond. the manager concludes that x has a normal distribution with mean of 10.2 millimeters and standard deviation of 1.4 milimeters. a. what is the probability that a single bream taken at random from the pond is between 8 and 12 millimeters long? b. what is the...

There are 10000 fishes in koorsala and the fish population obeys the logistic model with harvesting....

There are 10000 fishes in koorsala and the fish population obeys the logistic model with harvesting. per capita birth rate is 14% per year the people have been catching 400 fish per year for a long time. One year, due to new fishing equipment, the harvesting rate increases to 550 fish per year. Assuming they carry on with this increased harvesting rate, what will be the fish population in the long run? Give your answer correct to the nearest integer.

The Wisconsin Fish and Game Department stocked a lake with 30% catfish, 15 % bass, 40%...

The Wisconsin Fish and Game Department stocked a lake with 30% catfish, 15 % bass, 40% bluegill, and 15% Northern Pike. Five years later they took a random sample of 500 fish from the lake and found 120 catfish, 85 bass, 220 bluegill, and 75 Northern Pike. At the 5% level of significance, can we show that the distribution of fish changed over the 5-year interval? State and test appropriate hypotheses. State conclusions.

Constant Yield Harvesting. In this problem, we assume that fish are caught at a constant rate...

Constant Yield Harvesting. In this problem, we assume that fish are caught at a constant rate h independent of the size of the fish population, that is, the harvesting rate H(y, t) = h. Then y satisfies dy/dt = r(1 − y/K )y − h = f (y). (ii) The assumption of a constant catch rate h may be reasonable when y is large but becomes less so when y is small. (a) If h < rK/4, show that Eq....

A strawberry farmer will receive $37 per bushel of strawberries during the first week of harvesting....

A strawberry farmer will receive $37 per bushel of strawberries during the first week of harvesting. Each week after that, the value will drop $0.80 per bushel. The farmer estimates that there are approximately 129 bushels of strawberries in the fields, and that the crop is increasing at a rate of four bushels per week. When should the farmer harvest the strawberries (in weeks) to maximize their value? (Assume that "during the first week of harvesting" here means week 1.)...

Find a 95% confidence interval for predicting the mean length of fish in a particular pond...

Find a 95% confidence interval for predicting the mean length of fish in a particular pond if the sample data contained the following length in centimeters 23 45 43 34 26 36 67 45 43 55 53 42 87 65 45 51 53 54 54 48 49 54 53 52 54

Subjects