Question

Write an exponential equation for the following situation. The drug dosage is 500 mg the drug is eliminated at a rate of 5.2% per hour use d to equal the amount of the drug in milligrams and t time and hours

Answer 1

To represent the elimination of a drug at a rate of 5.2% per hour with an initial dosage of 500 mg, the exponential decay equation d = 500 × e-0.052t can be used, where d is the dosage at time t.

Step-by-step explanation:

To write an exponential equation for the situation where the initial drug dosage is 500 mg and the drug is eliminated at a rate of 5.2% per hour, we need to use the formula that represents exponential decay:

d = d0 × e-kt

Here, d represents the amount of the drug in milligrams at time t, d0 is the initial dosage, k is the decay constant (as a decimal), and t is the time in hours. The decay constant k for a 5.2% elimination rate per hour is 0.052, and thus the equation becomes:

d = 500 × e-0.052t

This equation will allow us to calculate the remaining dosage in the body after any given number of hours has passed.