A medication has a half-life of 4 hours after it enters the bloodstream. A nurse administers a dose of 225 milligrams to a patient at noon. Write an expression to represent the amount of medication, in milligrams, in the patient's body at: 1 p. m. on the same day 7 p. m. on the same day

The half life of a material is the time that a given quantity A of the material, decays into its half.

We know that the half-life is 4 hours, then we have the equation:

Q (t) = A*r^t

Where A is the initial quantity, and t is the number of hours.

and we have that r^4 = 1/2 (so when t = 4, we will have half of A)

then r = (1/2) ^ (1/4) = 0.84

Then our relation is

Q (t) = A*0.84^t

We have that A = 225mg,

at 1:00 pm. we have one hour after noon, so here we need to use t = 1.

Q (1) = 225mg*0.84^1 = 189.2mg

At 7:00 pm, we have 7 hours since noon, so here we need to use t = 7

Q (7) = 225mg*0.84^7 = 66.4mg