A body assimilates a 16-hour cold tablet at a rate modeled by , where C is measured in milligrams and t is the time in hours.Use Simpson's Rule with to estimate the total amount of the drug absorbed into the body during the 16 hours.

Question

A body assimilates a 16-hour cold tablet at a rate modeled by  ,  where C is measured in milligrams and t is the time in hours.Use Simpson's Rule with  to estimate the total amount of the drug absorbed into the body during the 16 hours.

Quizplus · Accepted Answer

Using Simpson's Rule with n=4, we have:

Δt = (16-0)/4 = 4

C_0 = f(0) = 0
C_1 = f(4) = 22.434
C_2 = f(8) = 32.245
C_3 = f(12) = 34.167
C_4 = f(16) = 24.45

Using the formula for Simpson's Rule, we get:

∫₀¹₆ C(t) dt ≈ (Δt/3) * [C₀ + 4C₁ + 2C₂ + 4C₃ + C₄]

≈ (4/3) * [0 + 4(22.434) + 2(32.245) + 4(34.167) + 24.45]

≈ 38.325

Therefore, the total amount of the drug absorbed into the body during the 16 hours is approximately 38.325 milligrams, which corresponds to choice C.

A Body Assimilates a 16-Hour Cold Tablet at a Rate