Question

For a certain drug, the rate of reaction in appropriate units is given by:

R' (t) = 4/t + 3/t^2+ e^t

where t is the time measured in hours after the drug is administered. The total reaction to the drug over the time period from the 5th hour to the 6th is approximately:_______

Answer 1

The approximate total reaction over the time period from the 5th hour to the 6th is therefore: 4ln(6) - 3/6 + e^6 - (4ln(5) - 3/5 + e^5).

Step-by-step explanation:

To find the total reaction to the drug over the time period from the 5th hour to the 6th, we need to calculate the definite integral of the rate of reaction function from 5 to 6. Given the rate of reaction function: R'(t) = 4/t + 3/t^2 + e^t, we can integrate it to find the total reaction.

The integral of 4/t is 4ln(t) and the integral of 3/t^2 is -3/t. The integral of e^t is e^t. Therefore, the integral of the rate of reaction function is: 4ln(t) - 3/t + e^t.

To find the total reaction over the time period from 5 to 6, substitute t = 6 into the integral function and subtract the result obtained when t = 5 is substituted into the integral function. The approximate total reaction over the time period from the 5th hour to the 6th is therefore: 4ln(6) - 3/6 + e^6 - (4ln(5) - 3/5 + e^5).