In 2007, (when t = 0), world solar photovoltaic (PV) market installations were 2826 megawatts and were growing exponentially at a continuous rate of 48% per year. Write a differential equation to describe the relationship in the form of dS/dt.

Q: The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: Given that rate of decay of radium is proportional to the amount present at that time.

Q: If the rate of change in the microwave rays M(x), where x is the distance, decreases with a rate…

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Q: Form the differential equation by elimanating the arbitary constant A,Bvfrom y=Ae7x+Be-7x

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Q: Initially 35 grams of radioactive substance was present. After 5 hours the mass had decreased by 11…

A: Given:- Initially 35 grams of radioactive substance was present. After 5 hours the mass had…

Q: Initially 50 grams of radioactive substance was present. After 6 hours the mass had decreased by 9%.…

A:

Q: The differential equation modeling population growth while incorporating the carrying capacity is =…

A: Given: Growth rate is 0.1 per year. Environmental limitation is of 4600 deer. Currently there are…

Q: can you give an example in real life, where differential equations are applied?

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Q: After t hours, the percentage of alcohol in the blood decays according to the differential equation…

A: After time t=9.555 hours....they can legally drive...for detail solution...go through the solution

Q: The rate growth of a population is proportional to the present population. If it is 1000 initially…

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

Q: Explain briefly the classifications of the Differential Equations?

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Q: Determine whether the following statement is true or false, and explain why. Every differential…

A: Solution:GivenEvery differential equation is either separable or linear.To determine the given…

Q: Initially 100 milligrams of a radioactive substance were present. After 6 hours the mass had…

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Q: If the number of sales is inversely proportional to the price of a product, write the differential…

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Q: After 2250 years, 25% of a radioactive material remains. If the rate of decay of the material is…

A: Half-life = 0.693/Decay constant(lambda)

Q: What is the differential equation given functions?

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Q: In the given question ,, determine whether the statement is true or false. If it is false, explain…

A: Given :                The function y = 0 is always a solution of a differential equation that can…

Q: If the rate of change in the microwave rays M(x), where x is the distance, decreases with a rate…

A: This question is about application of differential equation

Q: Identify the differential equation that produces the slope field below. // ||// // 2.

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Q: The number of customers in a store is modeled by the function P that satisfies the logistical…

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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: A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced…

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Q: If the number of fruit flies F increases at a rate that is proportional to the number of flies…

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

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Q: Calculate whether the differential equation is exact or not and Find the general solution.

A: The given differential equation is:x2+2x+ydx+2dy=0We need to check whether the equation is exact or…

Q: An individual improperly disposes of 8 parakeets in a nearby woodland, where they begin to reproduce…

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Q: Carbon extracted from an ancient skull combined only one-sixth as much as C14 as carbon extracted…

A: Let's find age of skull.

Q: To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t)…

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Q: The tank in the figure contains 4000 L of water in which initially 50 kg of salt is dissolved. Brine…

A: Given that, The tank contains 4000 L of water in which initially 50 kg of salt is dissolved. Brine…

Q: Is the logistic equation a linear differential equation?

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Q: The rate at which radioactive nuclei decays is proportional to the number of such nuclei that are…

A: Given Half of the original number of radioactivenuclei have undergone disintegration in a period of…

Q: The proportion of people in a community infected with a virus that stays active for two weeks is x…

A: The complete solutions are given below

Q: A radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of radium…

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Q: Solve the differential equation Y=3x+logP

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Q: Write the first-order linear differential equation in standard form?

A: Query- Write the first-order linear differential equation in standard form. Answer-  A linear…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

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Q: A colony of bacteria with originally 100 cells has now grown to 900 in 2 hours. Assuming the rate of…

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Q: If the rate of change in the number of cows, W, in a population is proportional to 150 - W(t), where…

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Q: find the differential equation of the family of logarithmic curves whose equation is Cy = ln(Cx).

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Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

A:

Q: What defines an One Differential Equation as linear or non-linear?

A: What defines an One Differential Equation as linear or non-linear?

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

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Q: Find the order and degree of the differential equation:

A: Given,                d2ydx2+5dydx4=13sinx

Q: Initially 48 grams of radioactive substance was present. After 6 hours the mass had decreased by…

A:

Q: Initially 47 grams of radioactive substance was present. After 10 hours the mass had decreased by…

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Q: In a nursery, the reason for spreading a virus epidemic is equal to half of those who have not…

A: Number of children infected N w.r.t to time t in days dNdt=N Use variable saprable method to solve…

Q: The rate of growth of wild horses is proportional to 2000 – H, where H is the number of horses and…

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Q: Barbara weighs 60 kg and is on a diet of 1600 calories per day, of which 850 are used automatically…

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Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

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Q: A certain bacteria culture is observed to double its amount after two hours it was initially…

A: Let say population is P. So population at time 't' is given by P(t). Assume initial population is P0…

Q: Initially 25 grams of radioactive substance was present. After 10 hours the mass had decreased by…

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.