The greater the daily dose of vitamin C patients take, the greater their plasma concentration of vitamin C becomes. This relationship increases at a rate of 0.1e^(-0.002 x) micromoles per milligram of daily dose. By approximately how many micromoles does the plasma concentration increase between x=100 and x=200 ? Choose 1 answer: (A) 0.067 (B) 0.15 (C) 7.42 (D) 33.5

Question

The greater the daily dose of vitamin  C patients take, the greater their plasma concentration of vitamin  C becomes. This relationship increases at a rate of  0.1e^(-0.002 x) micromoles per milligram of daily dose. By approximately how many micromoles does the plasma concentration increase between  x=100 and  x=200 ? Choose 1 answer: (A) 0.067 (B) 0.15 (C) 7.42 (D) 33.5

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Understand Relationship and Function: Understand the relationship between the daily dose of vitamin C and the plasma concentration. The relationship is given by the function f(x) = 0.1e^(-0.002x), where x is the daily dose in milligrams. We need to find the increase in plasma concentration between x=100 and x=200.Calculate Plasma Concentration at x=100: Calculate the plasma concentration at x=100. We substitute x=100 into the function to get f(100) = 0.1e^(-0.002*100).Perform Calculation for x=100: Perform the calculation for x=100. f(100) = 0.1e^(-0.2) ≈ 0.1e^(-0.2) ≈ 0.1 * 0.8187 ≈ 0.08187 micromoles.Calculate Plasma Concentration at x=200: Calculate the plasma concentration at x=200. We substitute x=200 into the function to get f(200) = 0.1e^(-0.002*200).Perform Calculation for x=200: Perform the calculation for x=200. f(200) = 0.1e^(-0.4) ≈ 0.1e^(-0.4) ≈ 0.1 * 0.6703 ≈ 0.06703 micromoles.Calculate Increase in Plasma Concentration: Calculate the increase in plasma concentration between x=100 and x=200. We subtract the plasma concentration at x=100 from that at x=200 to find the increase. Increase = f(200) - f(100) ≈ 0.06703 - 0.08187.Perform Subtraction for Increase: Perform the subtraction to find the increase. Increase ≈ 0.06703 - 0.08187 ≈ -0.01484 micromoles. This result is negative, which indicates a decrease rather than an increase. This is a math error because the plasma concentration should increase with an increase in the daily dose of vitamin C.

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