p=8/5−1/2500x Calculate E(p), the elasticity of demand, and use it to find the value of p for which E(p)=1. Give your answer as a decimal to one decimal place.

Q: A sample of radioactive material has a half-life of about 1200 years. An initial sample weighs 20…

A: Given half life of the radioactive sample is about 1200 grand initial sample weight is 20 grams.

Q: A population is growing according to the logistic model:- N = 5000/ 1 + e 4.8-1.9t where t is the…

A: Solution:Given N=50001+e4.8-1.9tFormula:Average poupulation over[a,b]P=1b-a∫abN(t)dt

Q: A radioactive substance is known to decay at a rate proportional to the amount present. In 2009…

A: Form a differential equation from the given problem to find solution.

Q: . The terminal value of an investment for T years at an annually compounded rate, r is given by VT =…

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Q: 1. The population of a town grows at the rate proportional to population present at any time t. The…

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Q: Find the capitalized cost C of an asset (a) for n = 5 years, (b) for n = 10 years, and (c) forever.…

A: Given, C0 = $ 700,000, c(t) = $25,000(1 + 0.08t), r = 0.06 Capitalized cost C, By substituting C0 ,…

Q: Calculate E(0.25), where E is the elasticity of demand. Give your answer to 3 decimal places.

A: Consider the given price-demand equation, p=85-12500xp=4000-x25002500p=4000-xx=-2500p+4000 Now,…

Q: Suppose the demand for a product is given by D(p) = Зр + 155. - A) Calculate the elasticity of…

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Q: 4. Determine the growth constant, k, of a population that is growing at a rate proportional to its…

A: let p=population at time t so we can write  to remove the proportionality sign we need to multiply…

Q: By natural increase, a city whose population is 40,000 will double in 50 yrs. There is a net…

A: This question is related to population growth, We will solve it using given information.

Q: Find dx/dp for the demand function. x=400/In(p^2+8)   (a) dx/dp =  (b) Interpret this rate 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: Find the present value P of a continuous income flow of c(t) dollars per year using c(t)e-rt dt, J-…

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Q: The logistic growth function f(t) = 140 / 1 + 9e-0.165t describes the population, f(t), of an…

A: Given: ft=1401+9e−0.165t,ft:represents population of an endangered species of elk t-years after they…

Q: The fish and game department in a certain state is planning to issue hunting permits to control the…

A: Given statement, The fish and game department in a certain state is planning to issue hunting…

Q: f the half-life of cesium-137 is 30 years, find the decay constant, r. (Round your answer to nine…

A: The relation between the half-life and decay constant is given by: t1/2=ln2k Given: t1/2=30 years

Q: describes the number of people, f(t), who have become ill With The logistic growth function f(t) =…

A: Here, the given function of the number of ill people after t weeks of outbreak is:…

Q: A commercial property generates income at the rate R(t). Suppose that R(0) = $70,000/year and that…

A: The formula to calculate the compound interest is given by: Compound Interest = Amount – Principal…

Q: 5. A bacteria colony grow at a rate of 11% per year. If the initial sample has a mass of 500 gram…

A: Initial mass of the bacteria P0=500 grams  growth rate r=11% per year =0.11 per year  Let size of…

Q: The logistic growth model P(t) 170 1+16-0.188t represents the population of a species introduced…

A: Given: The logistic growth model is Pt=1701+16e-0.188t represents the population of a species…

Q: Assume there is a certain population of deer in a forest whose growth is described by the logistic…

A: Given: Growth rate, r=0.56 Carrying capacity of the forest, k=10,000 Starting population, p0=5400…

Q: The time t (in years) required for an investment to double with interest compounded continuously…

A: Solution:Given    t(r)=ln 2rat r=3.5%To determine the length of time

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

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Q: A 10 year continuous annuity pays at a rate of t at time t. If v^t = .94t, calculate the accumulated…

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Q: Find the capitalized cost C of an asset (a) for n = 5 years, (b) for n = 10 years, and (c) forever.…

A: a) The required value is calculated as follows: C=700000+∫0525000e-0.06tdt…

Q: Suppose the demand for a product is given by D(p) – 4p + 136. A) Calculate the elasticity of demand…

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Q: Find the present value P of a continuous income flow of c(t) dollars per year using where t1 is the…

A: Given, c(t)=100,000+4000, r=5%, t1=10 p=∫0t1c(t)e-rtdt Now plug the values of t1  and r…

Q: Find the present value of a continuous income stream F(t) = 20 + 5t, where t is in years and F is in…

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Q: Find the present value of a continuous income stream F(t) = 40 + 5t, where t is in years and F is in…

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Q: The population of a certain country in 1998 was 280 million people. In addition, the population of…

A: To find the time in terms of year for which the population of the country reaches 312 million and…

Q: Assume that P(t) follows the logistic growth model, with a = 0.15 and b = 0.028. Assume that the…

A: givenP(t) Assumes logistic growth model and a=0.15 and b=0.028 and initial population p(0)=135To…

Q: The logistic growth function f(t) = 107.000 1+ 4500 e describes the number of people, f(t), who have…

A: This question is related to Functions, we will solve it using given information.

Q: Find the present value P of a continuous income flow of c(t) dollars per year using P = c(t)e-rt dt,…

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Q: Certain chemotherapy dosages depend on a patient's surface area According to the Mosteller model,…

A: Given that S=hw60, where h is the patient's height and w is the patient's weight.

Q: 7. dt Scientist has observed that a small colony of penguins on a remote Antarctic island obeys the…

A: As per the question we are given a population growth model of penguins as : dP/dt = rP Where P is…

Q: The logistic growth function f(t) = - describes the number of people, f(t), who have become ill with…

A: Topic = Algebra

Q: Strontium-90 is a radioactive material that decays according to the function A(t) = A, e -0.0244,…

A: According to our expert policy only three sub parts are to be answered

Q: ) Greenland had a population of 55000 in 1980 and a population of 78000 in 1990. Assume that the…

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Q: Strontium-90 is a radioactive material that decays according to the function A(t) = Ao e -0.0244t,…

A: Given : a.   Decay rate = -0.0244= -0.0244×100%= -2.44 %

Q: With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate…

A: ∫xndx = xn+1n+1 + C, where 'C' is the constant of integration.

Q: Consider the price-demand equation given by 8 x. 2, 500 Calculate E(0.25), where E is the elasticity…

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Q: The development of a new amusement park on the outskirts of a city is expected to increase the…

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Q: Strontium-90 is a radioactive material that decays according to the function A(t) = A e -0.0244t,…

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Q: A tank initially contains 400 gal of fresh water. At time t=0, a brine solution witha concentration…

A: We will find amount of solution after t min and then find time required to empty the tank  To find…

Q: The weekly sales of Honolulu Red Oranges are given by q = 1, 000 − 10p. Calculate the price…

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Q: The rate of investment is given by I (t) = 5vt. Calculate the capital growth between the 4th and the…

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Q: The weekly sales of Honolulu Red Oranges is given by q = 216 - p^2. Calculate the price elasticity…

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Q: Assume there is a certain population of deer in a forest whose growth is described by the logistic…

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Q: Suppose the demand for an item is x=10 +1/p2   Evaluate the elasticity at E(0.5)

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Q: Find the effective annual yield and the continuous growth rate if the value of a deposit is given by…

A: The deposit is given by

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.