Question

In: Math

Biologists stocked a lake with 400fish and estimated the carrying capacity (the maximal population for the...

Biologists stocked a lake with 400fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 7300. The number of fish grew to 620 in the first year.

a)Find an equation for the number of fish P(t) after t years

b)  How long will it take for the population to increase to 3650 (half of the carrying capacity)?
It will take ???? years.

Solutions

Expert Solution


Related Solutions

PART A) Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal...
PART A) 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 5300. The number of fish doubled in the first year. Assuming that the size of the fish population satisfies the logistic equation dPdt=kP(1−PK), 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)=______________ How long will it take...
The carrying capacity for a country is 800 million. The population grew from 282 million in...
The carrying capacity for a country is 800 million. The population grew from 282 million in the year 2000 to 309 million in the year 2010. 1) Make a logistical model for determining the country's population 2) Use this model to predict the country's population in 2100 3) Predict the year in which the population will exceed 500 million
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...
I have a logistic growth equation for a population where K = 820 carrying capacity, and...
I have a logistic growth equation for a population where K = 820 carrying capacity, and P(0) =550 initial population with a growth rate r of 0.25. Using the equation P= K/(1+A.e^-rt) i can find out the Value of A from initial conditions as A=(K-P(0))/P(0) and apply the equation to calculate values of P at different time intervals between 0 ans 12 years. If I have to use the same parameters as a logistic decay starting with an initial population...
Using the carrying capacity model recursively, k= 800 million, the population of the United States for...
Using the carrying capacity model recursively, k= 800 million, the population of the United States for each year between 1950-2017. 1950 population was 158804 thousand. What is the model’s predicted U.S. population for the year 1999 (in thousands)? the growth rate of 0.01078. Give your answer correct to the nearest whole number.
A certain elevator has a maximum legal carrying capacity of 6000 pounds. Suppose that the population...
A certain elevator has a maximum legal carrying capacity of 6000 pounds. Suppose that the population of all people who ride this elevator have a mean weight of 160 pounds with a standard deviation of 25 pounds. If 35 of these people board the elevator, what is the probability that their combined weight will exceed 6000 pounds? Assume that the 35 people constitute a random sample from the population.
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.
16. Which of the following best describes when a population has reached carrying capacity within an...
16. Which of the following best describes when a population has reached carrying capacity within an ecosystem (A) Birth rate= death rate (b) Population growth accuracy exponentially (c) Organism are adjusting to new environmental conditions (d) Birth rate exceed death rate
What role does ventilation play in determining maximal exercise capacity?
What role does ventilation play in determining maximal exercise capacity?
Consider a population of antelope, with P0=2,750, carrying capacity K=3,875, and growth rate r=0.073 (or 7.3%)...
Consider a population of antelope, with P0=2,750, carrying capacity K=3,875, and growth rate r=0.073 (or 7.3%) per year. Assuming that this population follows logistic growth, find P(t), then use the solution to predict the population after 8 years. Round your final answer to the nearest integer value and do not include units.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT