Question

You take 300 milligrams of headache medicine, and after 2 hours, 180 milligrams remain in your system. How long will it take from the time of the initial dose for the effects of the medicine to wear off, if this occurs when only 100 milligrams remain? (Assume the amount of medication in your system decays exponentially.) Round to the nearest hundredth of an hour.

Name: you take 300 milligrams of headache medicine and after 2 hours 180 milligrams remain in your system how long will it take from the time of the initial dose for the effects of the medicine to 11726
Uploaded: 2023-06-03T15:06:48-08:00
Duration: 1 min 53 s
Channel: Kathleen Carty
Description: you take 300 milligrams of headache medicine and after 2 hours 180 milligrams remain in your system how long will it take from the time of the initial dose for the effects of the medicine to 11726

          You take 300 milligrams of headache medicine, and after 2 hours,
180 milligrams remain in your system. How long will it take from
the time of the initial dose for the effects of the medicine to
wear off, if this occurs when only 100 milligrams remain? (Assume
the amount of medication in your system decays exponentially.)
Round to the nearest hundredth of an hour.

Added by Nicole R.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Kathleen Carty

06/03/2023

Step 1

We know that the amount of medication in the system decays exponentially, which means we can use the formula: A = A0 * e^(-kt), where A is the amount of medication in the system at time t, A0 is the initial amount of medication, k is the decay constant, and t is Show more…

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You take 300 milligrams of headache medicine, and after 2 hours, 180 milligrams remain in your system. How long will it take from the time of the initial dose for the effects of the medicine to wear off, if this occurs when only 100 milligrams remain? (Assume the amount of medication in your system decays exponentially.) Round to the nearest hundredth of an hour.