I have created a scatter plot and the exponential function I found is y = 30e-0.004t. I need help solving the rest of the questions. A brief explanation of each part will also suffice.
Codeine phosphate is a drug used as a painkiller. Generally, it is mixed with acetaminophen in tablet form. It is rapidly absorbed into the bloodstream from the gastrointestinal tract and is gradually eliminated from the body via the kidneys. A common brand contains 30 mg of codeine. Since it is physically addictive and has other unwanted side effects, it is important to avoid an overdose while helping to relieve pain symptoms such as those caused by a headache. Samples of blood were taken at regular time intervals from a patient who had taken a pill containing 30 mg of codeine. The amount of codeine in the bloodstream was determined every 30 min for 3 h. The data are shown in the table below.
Time after Consumption: Amount of Codeine in Blood:
30 min 27 mg
60 min 23.5 mg
90 min 21.2 mg
120 min 18.7 mg
150 min 16.6 mg
180 min 14.5 mg
Assume that the same equation applies to the second pill as to the first. Suppose the patient took a second pill 1 h after consuming the first pill.
Create a equation for the amount of codeine in the patient’s bloodstream t minutes after taking the first pill.
Determine the maximum amount of codeine in the patient’s bloodstream.
Determine when 90% of the maximum amount would be eliminated from the body.
