For any logistic equation, show that the point of inflection occurs at y = L/2 when the solution starts below the carrying capacity L.

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: Over the past fifty years the carbon dioxide level in the atmosphere has increased. Carbon dioxide…

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Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

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Q: Is the logistic equation separable?

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Q: A study of a certain Subanen community suggests thatt years from now, the average level of carbon…

A: Given query is to find the rate of change of carbon monoxide after 2 years.

Q: The half-life of the radioactive element tritium is 12 years. Find its decay constant.

A: We have, the half-life of the radioactive element tritium is 12 years. As we know that, The time in…

Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

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Q: When the price of a book is $125, a book store can expect to sell 600 books. If the price rises to…

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Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

A: Given,initial kangaroo number, n(0) = 200number of kangaroo after 3 years, n(3) =500carrying…

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

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Q: The growth in the number (in millions) of Internet users in a certain country between 1990 and 2019…

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

A: Given:    Half-life of radioactive cobalt =5.27 years    The proportion p that remains after y years…

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: Consider a population that begins growing exponentially at a base rate of 8​% per year and then…

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Q: The growth in the number​ (in millions) of Internet users in a certain country between 1990 and 2015…

A: The logistic function is given as, , where G0=initial number m= maximum possible number t=time…

Q: At the time of the birth of a child, a parent wants to begin a college fund that will grow to $43000…

A: Given that the interest is compounded continuously

Q: How long will it take to triple $12000, invested at 4.5% compounded continuously? (A = Pe*t) %3D

A: We are given the initial value to be $12000 and rate r = 4.5% = 0.045. Now, we need to find that how…

Q: Suppose that a particular pond can sustain up to 30,000 tilapia and that the undisturbed population…

A: The logistic model is given as: dP/dt = 4(1 - P/30000)P When P = 15000, we get, dP/dt = 4(1 -…

Q: What happens to the rate of change of the exponential function y = ax as a becomes larger?

A: To explain the given problem

Q: A radioactive substance decays at a rate proportional to the amount present ( y(t) = yoe-rt ) If 40%…

A: let the amount of radioactive material be x, and Given that…

Q: The radioactive isotope lead has a half-life of 3.3 hours and decays at a rate proportionate to the…

A: This is a problem of differential equation and integration. Based on the given scenario first of all…

Q: When a breeding group of animals is introduced into a restricted area such as a wildlife reserve,…

A: The number N of deer present at time (t) is given by Nt=12.350.01+0.54t    .....1

Q: What happens to the rate of change of the logarithmic function y = loga x as a becomes larger?

A: What happens to the rate of change of the logarithmic function y = loga x as a becomes larger?…

Q: One model for the way diseases die out when properly treated assumes that the rate dy/dt at which…

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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

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

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Q: b) Find the equation of the line tangent to the graph of y=log; (5x +1) at x = 2

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Q: A deposit earns interest at a rate of r percent compounded continuously and doubles in value in 10…

A: Given that, after 10 years, the initial amount is doubles, when the rate of interest r is compounded…

Q: The number N() of people In a community who are exposed to a particular advertisement is governed by…

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Q: city of half a million, there are initially 400 cases of a particularly virulent strain of flu. The…

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Q: In a study of a marine tubeworm, scientists developed a model for the time T (measured in years)…

A: Consider the provided question, The time required for the tube worm to reach a length L is given by,…

Q: What are the blanks?

A: Note: We are authorized to answer three sub-parts at a time. Since you have asked more than three…

Q: With a half life of 36 hours. Suppose a patient receives a  medication of 90 milligrams at midnight.…

A: A=A0e-ktAt t=36,A=A02A02=A0e-36kk=ln236A=A0e-ln236tA0=90At noon on first day…

Q: 4. A bank pays interest continuously at the rate of 6%. How long does it take for a deposit of Qo to…

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Q: g) For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a…

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Q: The annual world consumption of silver is predicted to be 22.3e0.0ir since 2014. Find a formula for…

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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: Sunset Lake is stocked with 2000 rainbow trout, and after 1 year the population has grown to 4500.…

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Q: Determine whether -log (1 when y = 0. Explain. –T) is a good cost function for logistic regression…

A: We need to find-whether -log 1-11+eθTx is a good cost function for logistic regression when y=0. For…

Q: If a village has a population of 2000 and a natural growth rate of 3.7% but has a carrying capacity…

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Q: When a breeding group of animals is introduced into a restricted area such as a wildlife reserve,…

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Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1" dollars per…

A: Given problem:- Find the PV of an income stream that pays out continuously at a rate of R(t) =…

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

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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: A radioactive material decays continuously at a rate proportional to the amount present. After 2…

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Q: Show that an investment that pays out R dollars per year continuously for T years has a PV of R(1…

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Q: When a breeding group of animals is introduced into a restricted area such as a wildlife reserve,…

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Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

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Q: Find the linearization of ƒ(x) = log3 x at x = 3. Then round its coefficients to two decimal places.

A: Given: f(x)=log3(x) at x=3

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.