The population of South Africa was 40,56 million in 1994 and 47,29 million in 2004. Assume this follows the logistic model with the carrying capacity of 250 million. Use the logistic equation to predict the population in 2050.

Q: The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2…

A: The exponential growth model is defined as, y = a(1 + r)t, where a is the initial amount, r is the…

Q: For letters B and C, use the logistic model P(t) =C/1+Ae^-kt 1. First, estimate the carrying…

A: Consider the given: Logistic Model of population of U.S.:Pt=C1+Ae−ktwhere, Pt=Population growthC =…

Q: Find a logistic function that satisfies the given conditions: y = 33 20 (0, 11) -20 (-2, 1) 20 40 2

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Q: The count of bacteria in a culture was 600 after 20 minutes and 2000 after 35 minutes.

A: 20,600 and 35,2000 Let the exponential model be y=abx. Substitute the given point to obtain the…

Q: In the first six months of the 2014 Ebola outbreak, the total number of reported cases was…

A: There were 100 cases as of April 2014 and it increases continuously at the rate of 72% per month.…

Q: Initially, there are 1 million bacteria present in a Petri dish. After 2 minutes, there are already…

A: given: Initially, there are 1 million bacteria present in a Petri dish.  After 2 minutes, there are…

Q: The population of bison in Canada was found to have a growth rate of  20%. If the If the population…

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Q: The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2…

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Q: Is the logistic equation separable?

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Q: What is the logistic equation? Why is it useful?

A: To write about the logistic equation and its use.

Q: Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population…

A: Given : Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal…

Q: According to worldometer.info, the world population in 2020 is 7, 794, 798, 739 and the population…

A: (1) In first part, we need to use population growth model which is given as follows P(t)=P0ektHere…

Q: At a suburban high school, information spreads by word of mouth according to the logistic function…

A: We are given an logistic function Here k is the growth rate and t is the time. Observe from the…

Q: Suppose that a population follows a logistic growth model.  The population in the first year is 21.7…

A: Given:    Data is given

Q: Suppose a population grows according to a logistic model with initial population 500 and carrying…

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Q: There were 210 million licensed drivers in the US in 2010 and 222 million in 2016.13 Find a formula…

A: For the given data of US licensed driver   210 million in 2010  222 million in 2016

Q: According to U.S. world census data, the world population in 1995 was 5,690,865,776 with a natural…

A: Logistic Model: A logistic model is used to model the population growth. In this model, the growth…

Q: Find the equation of the logistic function with a maximum value of 1000, an initial value of 500,…

A: Topic:- function

Q: Assume the carrying capacity of the earth is 11 billion. Use the 1960s peak annual growth rate…

A: According to the given information it is required to predict the base growth rate and current growth…

Q: A contagious disease is spreading in a town of 10,000 people. There were 200 infected people when…

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Q: Biologists stocked a lake with 700 fish and estimated the carrying capacity to be 9700. The number…

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Q: Suppose a population grows according to a logistic model with initial population 400 and carrying…

A: Given: Initial population =400 carrying capacity,M=10,000 P0=400 Formula used:

Q: If a piece of machinery depreciates continuously at an annual rate of 4%, how many years will it…

A: To find: The number of years it will take for the value of machinery to halve. Concept used: The…

Q: Suppose a population grows according to a logistic model with initial population 1000 and carrying…

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Q: In the year 2006, the age-adjusted death rate per 100,000 Americans for heart disease was 238.5. In…

A: (a) Let exponential model for the given data will be, Dt=D0e-λt, where Dtis death rate 100,000…

Q: If we are modeling a herd of clk, with an initial population of 100, in a region with a carrying…

A: Given that The population of elk satisfies a logistic growth model and  Initial population = 100…

Q: The population of the world was 5.28 billion in 1990 and 6.07 billion in 2000. Find an exponential…

A: Given information, Population of the world in 1990 P0=5.28 billion…

Q: 4. The population of the UK was 63.46 million in 2010 and 67.14 million in 2018. a. Find a logistic…

A: Givena)The population of UK in 2010 =63.46 millionsThe population of UK in 2018  =67.14 millions The…

Q: Because of an economic slump, a company finds that its annual profits have dropped from 700 thousand…

A: First we shall find profit function with setting intial time 2006

Q: Consider a population that begins growing exponentially at a base rate of 4.1​% per year and then…

A: Given that a population is begins growing exponentially at a base rate of  r=4.1% per year and then…

Q: Given that the population of the US was 151 million, 216 million, and 281 million in 1950, 1975, and…

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Q: Solve for when the population increases the fastest in the threshold logistic equation : 1000 P'(t)…

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Q: The City of Dallas had a population of 1,270,000 in 2010, and a population of 1,560,000 in 2020. It…

A: According to question given thatThe city of Dallas had a population of=1,270,000 in 2010And a…

Q: In the year 1998, the age-adjusted death rate per 100,000 Americans for heart disease was 235.9. In…

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Q: In Russia, the average consumer drank two servings of Coca-Cola in 1993. This amount appeared to be…

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Q: A field currently contains 22 mint plants. Absent constraints, the number of plants would increase…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Consider the following estimated model, where the dependent variable is the log of the hourly wage:…

A: Given: logwage=0.417+0.17educ+0.0295tenure-0.00059tenure2

Q: The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2…

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Q: Biologists stocked a lake with 300 fish and estimated the carrying capacity to be 9400. The number…

A:

Q: the logistic equation.

A: Ler Assume there is a certain population of fish in a pond whose growth is described by the logistic…

Q: A rumor is spreading on an island with a population of 50,000 individuals. When the rumor starts to…

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Q: Personal care aide is an occupation that is growing quickly. Assume that, in a certain region, tehre…

A: Consider that in 2014 the number of personal care aides is x.

Q: A species is considered to be endangered if it is expected to be extinct within 20 years. A…

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Q: Biologists stocked a lake with 600 fish and estimated the carrying capacity to be 7400. The number…

A: The form of the logistic equatIon is: y(t)=c1+aebt The carrying capacity is: 7400 Therefore c = 7400

Q: In the 2000 U.S. Census, a small city had a population of 55,000. By 2010, the population had…

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Q: Consider an island that is separated from the mainland, which contains a pool of potential colonizer…

A: Given that the rate of immigration of new species is given by the formula I=5.0×0.93t species per…

Q: Our new magazine initially sells 200 copies per month. Research indicates that a vigorous…

A: Givennumber of copies initially sell =200 per monthgrowth rate is 30% each monthThe upper limit for…

Q: Solve for when the population increases the fastest in the threshold logistic equation : 1000 P'(t)…

A:

Q: Personal care aide is an occupation that is growing quickly. Assume​ that, in a certain​ region,…

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Q: Suppose 19 blackberry plants started growing in a yard. Absent constraint, the blackberry plants…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.