132k views
3 votes
Need some help, please

800 mg of a medication is administered to a patient. After 4 hours, only 318 mg remains in the bloodstream. If the decay is continuous, what is the continuous decay rate (as a percentage)?
--------------- %

User SteveEdson
by
8.3k points

1 Answer

7 votes
We can use the formula for continuous decay to find the decay rate as a percentage:

A = Pe^(rt)

where:
A = the amount remaining after time t
P = the initial amount
r = the continuous decay rate
t = time

In this case, the initial amount is 800 mg, the amount remaining after 4 hours is 318 mg, and we want to find the continuous decay rate (r) as a percentage.

First, we need to find the time in hours since the decay is given per hour.

t = 4 hours

Next, we can plug in the values we know into the formula:

318 = 800e^(4r)

Solving for r:

e^(4r) = 318/800
4r = ln(318/800)
r = ln(318/800)/4

r ≈ -0.0575

The continuous decay rate is approximately -0.0575.

To convert this to a percentage, we can multiply by 100:

r as a percentage ≈ -5.75%

Therefore, the continuous decay rate is approximately 5.75%.
User Enselic
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories