To find the total reaction to the drug over the specified time periods, we need to integrate the rate of reaction function R'(t) with respect to t over the given intervals.
a. From t=1 to t=11:
∫[1, 11] (3/t + 1 + 3/(t+1)^1/2) dt
= 3ln|t| + t + 6√(t+1) |[1, 11]
= 3ln|11| + 11 + 6√12 - 3ln|1| - 1 - 6√2
= 3ln(11) + 11 + 6√12 - 3 - 6√2
≈ 16.63
b. From t=11 to t=24:
∫[11, 24] (3/t + 1 + 3/(t+1)^1/2) dt
= 3ln|t| + t + 6√(t+1) |[11, 24]
= 3ln|24| + 24 + 6√25 - 3ln|11| - 11 - 6√12
= 3ln(24) + 24 + 30 - 3ln(11) - 11 - 6√12
≈ 38.59
Therefore, the total reaction to the drug from t=1 to t=11 is approximately 16.63 and from t=11 to t=24 is approximately 38.59.
For a certain drug, the rate of reaction in appropriate units is given by
R’(t)=3/t+1+3/(t+1)^1/2
Where t is time and hours after the drug is administered. Find the total reaction to the drug over the following time periods.
a. From t=1 to t=11
B From t=11 to t=24
1 answer