Question

Jana is prescribed 250 mg of medication. Seventy-five percent of the medication remains in her body after each hour, h, according to the equation mc019-1.jpg. Six hours later, Allison is prescribed the same medication. The medication remains in Allison’s body according to the equation mc019-2.jpg. At any time after she has taken the medication, Allison has how many times more milligrams of medication in her body?

I'll edit the question in just a minute so the formulas are in it

Answer 1

Jana was prescribed medication. m = 250(0.75)^h

6 hours after Jana took her medication, Allison was prescribed the same.
m=250(0.75)^(h-6)

At any time after she has taken the medication, Allison has how many times more milligrams of medication in her body?

Same with Jana, Allison's medication content in her body will decrease by 25% after each hour.

Let h = 6

Jana: m = 250(0.75)^6 = 250(0.178) = 44.50
Allison: m = 250(0.75)^6-6 = 250(1) = 250

250 - 44.50 = 205.50

On hour 6, Allison will have 205.5 mg more of the medicine than Jana.