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- Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.Suppose that the growth-rate parameter k = 0.3 and the carrying capacity N = 2500in the logistic population model of Exercise 17. Suppose P(0) = 2500.(a) If 100 fish are harvested each year, what does the model predict for the longtermbehavior of the fish population? In other words, what does a qualitativeanalysis of the model yield?(b) If one-third of the fish are harvested each year, what does the model predict forthe long-term behavior of the fish population?A particular specie of animal has a carrying capacity of K and a growth rate of r. From an initial population of N0, what will be its population after a very long time? Show your calculations.
- A particular specie of animal has a carrying capacity of K and a growth rate of r. From an initial population of N0, what will be its population after a very long time? Show your complete calculations.During the start of the COVID 19 pandemic it is assumed that the rate of spread of the corona virus is 18 % daily following a simple logistic growth model by Verhulst. Ten persons are assumed to have acquired the virus in province X. Assuming province X with a population of 2 million does not follow any necessary protocol to prevent the spread of the virus, approximately how many are expected to have acquired the virus after 30 days?The population of the world in 2015 was 9.75 billion people and was growing at a rate of1.25% per year. (i) Assuming that this growth rate continues, derive a model to represent thepopulation P (in billions of people) in year t. (ii) From the model derive in (i), approximately when will the population of theworld be 11.2 billion people?
- An animal has an initial population of No. From that initial population count, it grew to 705 individuals after 25 years. After 25 more years, the population rose to 2500 individuals. If the carrying capacity for this particular specie is 2700 individuals. Calculate the initial population and the growth rate constant of the said species.An individual improperly disposes of 8 parakeets in a nearby woodland, where they begin to reproduce at an initial rate of 3 parakeets per month. Write a differential equation for the population P assuming logistic growth, where the woodland can support at most 500 parakeets. (Do not round any coefficients.) dP/dt =The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per year. Required: Assuming that this growth rate continues, derive a model to represent the population P (in billions of people) in year t. Approximately when will the population of the world be 11.2 billion people?
- Suppose COVID-19, a pandemic that spread worldwide has infected 40,000 people on August 2020. Each day, the number of infected is estimated to be 300. Assuming that the number of daily infections are constant, 1. What is the monthly growth rate of infection k? Assume time t is measured in months. 2. How many persons will be confirmed positive by the end of December 2020? 3. Assuming that there has a turn of events and a vaccine is discovered by September 2020. In addition, the number of cases dropped with the number of recoveries at a rate of 100 per day. There have been no additional cases after September. How much time t will elapse for the cases of COVID-19 to drop to 500?The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per year. i. Assuming that this growth rate continues, derive a model to represent the population P (in billions of people) in year t. ii. From the model derive in (i), approximately when will the population of theworld be 11.2 billion people?The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 2.6% per hour. How many hours does it take for the size of the sample to double?