Use the following model for the next two questions: The C(t) of a drug administered to a patient intravenously jumps to its highest level almost immediately. The concen- tration subsequently decays exponentially according to the law C(t) = Coet where C(0) = Co. The physician administering the drug would like to have m < C(t) < M, where m is the concentration below which the drug is ineffective and M is the concentration above which the drug is dangerous. (a) Suppose that immediately after a certain drug is administered, the concentration is 5 milligrams per milliliter. Ten hours later the concentration drops to 1.5 milligrams per milliliter. Determine the value of k for this drug.

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

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Q: The population of a community grows in proportion to the population at any time t. Its initial…

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Q: The population of a culture of bacteria is modeled by the logistic equation P(t) = 14,250/ 1 + 29e…

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Q: y = log, x is equivalent to the exponential form %3D x > 0, b > 0, b # 1.

A: To fill in the blanks

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A: dPdt=0.067P(t)dPP(t)=0.067dt∫P0PdPP(t)=∫0t0.067dtln|P(t)|-ln|P0|=0.067tlnP(t)P0=0.067tP(t)P0=e0.067t…

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Q: If m is an exponential function with a decay factor of 0.041 and m(0) = 200, solve for m(2).

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Q: Suppose that Po is invested in a savings account in which interest is compounded continuously at 6…

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Q: Find the exponential function f(x)=ab^x that satisfies the conditions f(0)=−3 and f(3)=−24

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Q: e the deer population P (t) in a small forest satisfies the logistic equation  ​dPdt  =  0.0225P −…

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Q: In Exercises, sketch the shifted exponential curves y = -1 - ex and y = -1 - e-x

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Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) = - M1+tanh 2 satisfies the…

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Q: Find the order of growth for the following function.  = (7n^5) + (2n^3) (log(n))

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Q: Find the exponential function of the form y=ab^x  that goes through the points (1,2) and (5,250)

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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.