Q.4 In some chemical reactions, the rate at which the amount of substance changes with time is proportional to the amount present. For the change of d-glucono lactone into gluconic acid, for example, dy = -0.6y dt when t is measured in hours. If there are 100g of ô-glucono lactone present when t=0, how many grams will be left after the first hour?

Q: 1. A spherical balloon is being filled with helium such that its radius is changing at a constant…

A: Given,            A spherical balloon is filled with helium gas and radius is increasing with rate…

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A: integration

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A:

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A: we have to find out

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A:

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A:

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A:

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A: (a)

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A: 1st we will formed a differential equation for amount of C and then solve it to get actual amount of…

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A:

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A:

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A: The solution is given as

Q: The rate of growth of the population N(t) of a new city t years after its incorporation is estimated…

A: dNdt=900+300tdN = (900+300t)dtIntegrating both side∫dN = ∫900+300t12dtN = 900t + 300 t12+112+1+C =…

Q: Starting with an initial value of P(0)= 55, the population of a prairie dog community grows at a…

A: The population of a prairie dog community grows at a rate of P'(t)= 20 - t/5 (prairie…

Q: 39. A population P, grows at the rate P'(t) = 5(t +1) In /t +1 %3D thousand individuals per year at…

A:

Q: Q13. A rain drop falling vertically under gravity gathers moisture from the atmosphere at a rate…

A:

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A:

Q: 10 If w'(t) is the rate of growth of a child in pounds per year, what does w'(t) dt represent? O The…

A:

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find in terms…

A:

Q: -5u where u du (ii) The rate of decay of a radioactive is given by dt is the material and is the…

A: du/dt = -5u Hence, du/u = -5dt Integrate both sides to get: lnu = -5t + C where C is the constant of…

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A: Given that initially, number of bacteria present in the culture is P0 At t=1, number of…

Q: 4. For infants less than 9 months old, the relationship between the rate of growth R (in…

A:

Q: 3. A hot coffee with temperature 90° C is placed in living room with temperature 26°C. After 5…

A:

Q: The rate of change of x is proportional to x. When t = 0, x0 = 3 and when t= 2, x = 6. What is the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: Given: The period T of Oscillations of a simple pendulum of length L is given by: where L is in…

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A:

Q: A cake is removed from an oven and its temperature is 350°F. Assume room temperature is 70°F. Five…

A: Given that the initial temperature of the cake is 350°F and after 5 minutes temperature varies to…

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A:

Q: 9. A model used for the yield Y of an agricultural crop as a fur tion of the nitrogen level N in the…

A: Please check step 2 for the solution.!

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A:

Q: Starting with an initial value of P(0)=55, the population of a crow community grows at a rate of…

A:

Q: When a vertical beam of light passes through a transparent medium, the rate at which its intensity I…

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A:

Q: d. Suppose that the cylindrical tank in the accompanying figure is filled to a depth of 4 feet at…

A:

Q: ! d. Suppose that the cylindrical tank in the accompanying figure is filled to a depth of 4 feet at…

A:

Q: (b) If n'(t) is the growth rate of a bee population in bees per week, what does n'(t)dt represent?

A: Given,n'(t)=growth rate of bee populationt=time in weeks

Q: 8) The rate (in mg carbon/m/h) at which photosynthesis takes place for a species of phytoplankton is…

A: Given:

Q: A rate of change of H is given by Solve for k where H> -25. O 0.458 0.346 0.255 0.144 ап = k (25 +…

A: This question can be solved using the concept of differential equation.

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A: The linear differential equations can be solved by separation of variables. The variables are…

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A:

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A:

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A: Population growth at a rate P’(t) = 500te-0.2t2 Where P(t) is the population after t months Evaluate…

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A:

Q: A. How many new bacteria will be in the culture after the first six hours? B. How many new bacteria…

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A: The given equation is: dP/dt = k√t.

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A: To find the rate of change of volume of the given container.

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A: