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.
A) 34.878
B) 46.878
C) 38.325
D) 54.325
E) 58.878

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.
A) 34.878 
B) 46.878 
C) 38.325 
D) 54.325 
E) 58.878

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