The initial population size of rock ptarmigans in an area is 500 ptarmigans. The growth rate is 0.2 and the carrying capacity is 8000 ptarmigans. The authorities in the area have announced that it is possible to start hunting in the area when the size of the population has reached 5000 ptarmigans. Assume that time is measured in years. After how many years can a ptarmigan be allowed to hunt in the area if we assume that the population size is in accordance with the logistic equation? )?

Q: A bacterian culture has a initial population of 10000. If its population declines to 5000 in 6…

A: Exponential model ⇒Pt=Ae-kt⇒A=initial population ⇒k=decay rate ⇒t=Time in hours⇒Pt=Population at…

Q: A. _1. y = 4*1 _2. y = 4*1 _3. y = 4% – 1 _4. y = -4* + 1 E. 5. y = 4*+1+ 1 D.

A: We find graph corresponding to first three exponential functions. 1. y=4^(x-1)  2. y=4^(x+1)  3.…

Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the population…

A: Consider the following exponential function: y=abx                                  ...... 1 Here,…

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

A: Given information:The number of personal care aids in 2024 is 157,500, which is a growth of 28% over…

Q: A species of beetles grows 41% every year. Suppose 100 beetles are released into a field construct…

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Q: The population of minnows in the lagoon is 5,400, but the population will decay exponentially. If…

A: The formula for the exponential decay model is, y=C1-rt Here, y is the final amount C is the initial…

Q: A bacteria decreases at a rate of 15% continuously when exposed to ultraviolent light. If a culture…

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Q: A bacteria culture under pressure has started to dissipate in size. The bacteria culture started…

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Q: The half-life of a substance is 1200 years. If the initial amount of the substance is 300 grams,…

A: Given ,Half life of  substance is 1200 years. Initial amount of substance = 300 grams. We model a…

Q: Suppose 16 blackberry plants started growing in a yard. Absent constraint, the blackberry plants…

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Q: A small town is known to grow its population at a rate proportional to the population at any time.…

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Q: The half-life of nickel-63 is 100 years. A students says, “An artifact with nickel-63 in it will…

A: Half life of a material means that the time required to reduce the initial quantity of the material…

Q: The population of a certain town is known to increase at a rate proportional to the number of people…

A: Let the population at time t be 'P' Now, as per the given data dPdt∝P⇒dPdt=kP

Q: If the population of a Nigeria doubles in 9 years, find the growth rate k. Assume that the population…

A: So the equation for the exponential population with growth rate k is given by: Where, A= initial…

Q: In 1986 the Chernobyl nuclear power plant exploded, and scattered radioactive material over Europe.…

A: Please check step 2 for the solution.

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.