A dennis word problem

[Guest]

I don't get how to do this, and the answers to these questions >.<

Dennis must take 250 mg of sinus medication every 12 h. Only 25% of the medication remains in his body by the time he takes the next dose.

a) At what level will the mass of the medication become constant?



b) How long will it take for the medication to reach this level?



thanks for your time,
Anna

 

[tkhunny]

Walk through it.

Time = 0 hours

250 mg

Time = 12 hrs

250 mg * 0.25 + 250 mg = 62.5 mg + 250 mg = 312.5 mg

Time = 24 hrs

312.5 mg * 0.25 + 250 mg = 78.125 mg + 250 mg = 328.125 mg

Time = 36 hrs

328.125 * 0.25 + 250 mg = 82.03125 mg + 250 mg = 332.03125 mg

Time = 48 hrs

332.03125 mg * 0.25 + 250 mg = 83.0078125 mg + 250 mg = 333.0078125 mg

Time = 60 hrs

333.0078125 mg * 0.25 + 250 mg = 83.251953125 mg + 250 mg = 333.251953125 mg

OK, I'm starting to formulate an idea. I'll do one more to confirm my suspicions.

333.251953125 * 0.25 + 250 mg = 83.31298828125 mg + 250 mg = 333.31298828125 mg

Yup. I'm pretty sure. The "old" piece seems to be approaching 250/3 = 83.333333333... The total stable value appears to be approaching 1000/3 = 333.333333333...

1) I haven't PROVEN anything, only suggested.
2) I haven't answered the questions.

A) The medication mass NEVER becomes stable. It ALWAYS oscillates between 250/3 and 1000/3. The MAXIMUM and MINIMUM levels do stabilize.
B) It doesn't. It's an asymptotic process.

Oh, let's do one more, just for fun.

Time = 72 hours

333.31298828125 mg * 0.25 + 250 mg = 83.3282470703125 mg + 250 mg = 333.3282470703125

It's lookin' good...