Suppose that the concentration C in mg/L of medication in a patient\'s bloodstre

Question

Suppose that the concentration C in mg/L of medication in a patient's bloodstream is modeled by the function C(x,t)=0.2x(e?0.2t?e?t), where x is the dosage of the medication in mg and t is the number of hours since the beginning of administration of the medication.

(a) Estimate the value of C(27, 3) to two decimal places.

C(27, 3) =

(b) If the dosage is 150 mg, give a formula for the concentration as a function of time t.

C(150, t) =

(c) Give a formula that describes the concentration after 1 hour in terms of the dosage x.

C(x, 1) =

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Suppose that the concentration C in mg/L of medication in a patient's bloodstream is modeled by the function C(x,t)=0.2x(e?0.2t?e?t), where x is the dosage of the medication in mg and t is the number of hours since the beginning of administration of the medication.

(a) Estimate the value of C(27, 3) to two decimal places.

C(27, 3) =

mg/L

(b) If the dosage is 150 mg, give a formula for the concentration as a function of time t.

C(150, t) =

(c) Give a formula that describes the concentration after 1 hour in terms of the dosage x.

C(x, 1) =

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Explanation / Answer

C(x,t)=0.2x(e0.2tet)

a)C(27, 3) =0.2*27(e0.2*3e3)

C(27, 3) =2.69 mg/L

b)C(150, t) =0.2*150(e0.2tet)

C(150, t) =30(e0.2tet)

c)

C(x, 1) = 0.2x(e0.2*1e1)

C(x, 1) = 0.2x(e0.2e1)

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