Answer :
The question is about Calculus and the task is the definite integral of the equation '2t + 8' from t = 5 to t = 8. The solution is found by integrating the equation and then subtracting the respective values obtained by substituting t = 5 and t = 8, which result is 24.
The total reaction to the drug from t=5 to t=8, you need to calculate the definite integral of the rate of reaction function R(t) with respect to t over the interval [5, 8]. The formula for calculating the definite integral is:
∫[a, b] R(t) dt
In this case, R(t) = 2/8 + t. Plug in the values and integrate:
∫[5, 8] (2/8 + t) dt
Integrate the terms separately:
∫[5, 8] 2/8 dt + ∫[5, 8] t dt
Now integrate each term:
(2/8) * ∫[5, 8] dt + (1/2) * ∫[5, 8] t dt
Simplify:
(1/4) * [t] from 5 to 8 + (1/2) * [t^2/2] from 5 to 8
Now plug in the values:
(1/4) * (8 - 5) + (1/2) * [(8^2 - 5^2)/2]
Calculate:
(1/4) * 3 + (1/2) * [(64 - 25)/2]
(3/4) + (1/2) * (39/2)
3/4 + 39/4
(3 + 39) / 4
42 / 4
10.5
So, the total reaction to the drug from t=5 to t=8 is 10.5 units.
Now, round the answer to the nearest hundredth:
10.5 rounded to the nearest hundredth is 10.50.
The correct answer is not among the options provided. The closest option is:
A) 24.58
However, none of the provided options match the calculated result of 10.50. It's possible that there's an error in the question or the options.
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Question: "For a certain drug, the rate of reaction in appropriate units is given by R(t) = 2/8 + t, where t is measured in hours after the drug is administered. Find the total reaction to the drug from t=5 to t=8. Round the answer to the nearest hundredth.
A) 24.58
B) 14.43
C) 39.1
D) 28.86"
