A worker at a hazardous waste plant was accidentally exposed to toxic chemicals which were absorbed...

 

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A worker at a hazardous waste plant was accidentally exposed to toxic chemicals which were absorbed into his bloodstream. Upon feeling ill, the worker went to a hospital and had some blood drawn for testing. The concentration of chemical in the drawn blood was found to be .0158 mg/ml. Expensive medication was administered to counter the effects of the chemical in the blood, but the doctor on duty knew that the concentration of the chemical in the bloodstream would have to decrease gradually over time according to the Basic Law of Exponential Decay (Ce). Medication would have to be administered every hour until the concentration was below .0050 mg/ml. Two hours later, blood was again drawn, and it was found to contain a chemical concentration of .0126 mg/ml. The doctor asked a lab technician to do the following. (You do the same): a. Write the particular solution for exponential decay for the chemical in the patient's blood. (Let = 0 represent the time that blood was first drawn.) b. Sketch a graph of the function from Part a. c. Find out how long it will be before the patient can be taken off medication. d. When the patient has only a negligible amount of chemical in his bloodstream (less than .0001 mg/ml), he can be released from the hospital. Find out how long the patient has to be hospitalized (from the time he first came to the hospital and had his blood drawn). e. Occasionally, patients exposed to this chemical suffer damage to their central nervous systems. A maximum concentration of .020 mg/ml requires a follow-up examination. The doctor estimated that the maximum concentration of the chemical in the worker's bloodstream occurred 1 hour after exposure. The patient estimated 1 hour after exposure would have been about 3 hours prior to his blood being drawn for the first time. Should the patient be asked to return for a follow-up exam? Why or why not? f. Find the half-life for the chemical in the bloodstream for the patient. A worker at a hazardous waste plant was accidentally exposed to toxic chemicals which were absorbed into his bloodstream. Upon feeling ill, the worker went to a hospital and had some blood drawn for testing. The concentration of chemical in the drawn blood was found to be .0158 mg/ml. Expensive medication was administered to counter the effects of the chemical in the blood, but the doctor on duty knew that the concentration of the chemical in the bloodstream would have to decrease gradually over time according to the Basic Law of Exponential Decay (Ce). Medication would have to be administered every hour until the concentration was below .0050 mg/ml. Two hours later, blood was again drawn, and it was found to contain a chemical concentration of .0126 mg/ml. The doctor asked a lab technician to do the following. (You do the same): a. Write the particular solution for exponential decay for the chemical in the patient's blood. (Let = 0 represent the time that blood was first drawn.) b. Sketch a graph of the function from Part a. c. Find out how long it will be before the patient can be taken off medication. d. When the patient has only a negligible amount of chemical in his bloodstream (less than .0001 mg/ml), he can be released from the hospital. Find out how long the patient has to be hospitalized (from the time he first came to the hospital and had his blood drawn). e. Occasionally, patients exposed to this chemical suffer damage to their central nervous systems. A maximum concentration of .020 mg/ml requires a follow-up examination. The doctor estimated that the maximum concentration of the chemical in the worker's bloodstream occurred 1 hour after exposure. The patient estimated 1 hour after exposure would have been about 3 hours prior to his blood being drawn for the first time. Should the patient be asked to return for a follow-up exam? Why or why not? f. Find the half-life for the chemical in the bloodstream for the patient.