Question

A patient takes 75mg of a medication every 12 hours; 60% of the medication in the blood is eliminated every 12 hours. (a) Let dn equal the amount of medication (in mg) in the bloodstream after n doses, where d1 = 75. Find a recurrence relation for dn.

Answer 1

The recurrence relation is dn = 0.4d(n-1) where d1 = 75

How to determine the recurrence relation?

The given parameters are:

• Initial, d1 = 75
• Rate of elimination, r = 60%

Since, the medication is eliminated from the blood; then it means that the function is an exponential decay function.

This is represented as:

d(n) = d(n - 1) * (1 - r)

Substitute r = 60%

d(n) = d(n - 1) * (1 - 60%)

Evaluate the difference

d(n) = d(n - 1) * 0.4

Evaluate the product

dn = 0.4d(n-1)

Hence, the recurrence relation is dn = 0.4d(n-1) where d1 = 75

Read more about exponential functions at:

https://brainly.com/question/27822382

#SPJ1