An exponential decay function A(t) = 600(1 - 0.29)^t models the situation. After 5 hours, there would be approximately 174.16 mg of ibuprofen in the system. It would take about 12.74 hours for the amount of ibuprofen to reach 30 mg.
To address your questions regarding ibuprofen decay in an adult's system, we need to employ exponential decay models. Let's start with part a) of your assignment.
Exponential Decay Function
The standard formula for exponential decay is A = P(1 - r)^t, where:
A is the amount remaining after time t.
P is the initial amount.
r is the decay rate per time interval.
t is the number of time intervals that have passed.
In this case:
P = 600 mg (the initial dose)
r = 0.29 (the decay rate, or 29%)
Therefore, the function modeling our situation is:
A(t) = 600(1 - 0.29)^t
Amount After 5 Hours
Plugging in t = 5 into the function, we get:
A(5) = 600(1 - 0.29)^5
A(5) is approximately 174.16 mg remaining after 5 hours.
Time to Reach 30mg
For part c), we want to find out when A(t) equals 30 mg. We set up the equation as follows:
30 = 600(1 - 0.29)^t
Solving for t, we get:
t ≈ 12.74 hour
It takes approximately 12.74 hours for the ibuprofen level to drop to 30 mg.