A hypothetical population of rats has an initial population of I = 400, the Carrying Capacity for their environment is K =10,000 and the constant of proportionality for the rat population is k = 3/4. Use the logistic growth model to estimate the rat population after 4 years. HINT: Use the model P=K/(1+Ae^(-kt) ) ,A= (K-I)/I  with e≈2.7182

Q: A certain radioactive material decays at a rate proportional to the amount present. At time ?=0,…

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

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A: Let's find time to take 90% of the lead to decay.

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A: Given, certain radioactive material is known to decay at a rate proportional to the present amount.…

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Q: The radioactive isotope Carbon-14 has a half-life of 5,730 years. Given 300 grams of C-14, what is…

A: topic - exponential function

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A: To use the given data (exponential model) to determine the initial data

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A:

Q: Suppose that a population grows according to a logistic model with carrying capacity 6500 and k =…

A:

Q: What rate of interest compounded continuously will yieldan effective interest rate of 6%?

A: It is given that, the effective interest rate is 6%. re=6%=0.06

Q: Today there are 500 ants on an colony. They breed with a constant continuous growth rate of 20% per…

A: We will find out the required solution.

Q: sample of a radioactive isotope had an initial mass of 490 mg in the year 1995 and decays…

A: Given: Initial mass of the isotopes in the year 1995 is 490 mg.            In 1998, sample's mass…

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

A:

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

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Q: A CERTAIN RADIOACTIVE MATERIAL IS KNOWN TO DECAY AT A RATE PROPORTIONAL TO THE AMOUNT PRESENT. IF…

A: Given that, after one hour, the 10% of the material is decayed. find the expression of the material…

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A:

Q: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. What is the…

A: Given: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. To…

Q: Suppose the rate of net investment is given by I (t) = Lnt, find the total capital accumulation…

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Q: Interest is compounded continuously at 5%.  How long until a $5000 investment grows to $12000?

A: Interest is compounded continuously at 5% $5000 investment grows to $12000

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Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

A: Topic-basic maths

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

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Q: Find the amount after 3 years if $ 1000 is invested at an intrest rate of 12% per year, compounded…

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

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Q: The number of bacteria in a certain population increases according to a continuous exponential…

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Q: The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

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Q: 4. The population of Lalaland is 600,000 currently and is expected to grow (continuously) at 3.5%…

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Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Of the 1000…

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Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

Q: A quantity with an initial value of 870 decays continously at a rate of 0.75% per day. What is the…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Given a certain radioactive material is known to decay at a rate proportional to the amount present.…

Q: An environmental study of a certain community suggests that t years from now the level of carbon…

A: Let's find.

Q: a certain radioactive material is known to decay at a rate proportional to the amount present. if…

A:

Q: At the beginning of the COVID-19 pandemic, the number of new cases was growing exponentially. There…

A: According to the guidelines issued by the company We are supposed to answer only first three…

Q: Suppose a population grows according to a logistic model with initial population 200 and carrying…

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Q: A quantity with an initial value of 8200 grows continuously at a rate of 0.55% per decade. What is…

A: Initial Value=  8200. Growth rate= 0.55% . We can formulate the following equation for "t" years :…

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Q: If 26 grams of radioactive waste reduces to 19.35 grams of radioactive waste after 1120 years, then…

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Q: In March 1976 the world population reached 4 billion. At that time, a popular news magazine…

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Q: At the beginning of the COVID-19 pandemic, the number of new cases was growing exponentially. There…

A: (a) Let  the exponential function for covid-19 growth is: Pt=a0bt      ......(1) Given a0=684 and b…

Q: A quantity with an initial value of 3600 grows continuously at a rate of 2.5% per decade. What is…

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Q: Suppose a variable is growing continuously at a nominal rate of 10% per year. What is the effective…

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Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A: Let Q  = amount of substance present            dQdt=kQ             integrating on both sides…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: The decay rate is proportional to the amount present. So, dNdt=-λN⇒dNN=-λdt⇒∫dNN=-λ∫dt+C⇒ln…

Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a…

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A: Given- Half life t12 =3.3 hours, Intial weight=1 gm. To find- The time in which the radioactive…

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A:

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.