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1. The half-life of a drug is an estimate of the period of time it takes for the concentration of the drug in the body to be reduced by exactly one half. Suppose the concentration C in mg/ml of a certain medication in terms of its half- life can be modeled by the function C(t) = A( where A represents the initial dose of the medication in mg and t represents the number of hours since the initial dose. a. If 20 mg of the medication was initially administered to a patient, what would be the concentration of the medication in 12 hours? b. C. Suppose the medication was administered 24 hours ago. If the concentration in the bloodstream is now 2 mg/ml, what was the initial dose? What does the function C(t) imply about the half-life of this particular medication? That is, how long will it take for the concentration of the drug to be cut in half?

1. The half-life of a drug is an estimate of the period of time it takes for the concentration of the drug in the body to be reduced by exactly one half. Suppose the concentration C in mg/ml of a certain medication in terms of its half- life can be modeled by the function C(t) = A( where A represents the initial dose of the medication in mg and t represents the number of hours since the initial dose. a. If 20 mg of the medication was initially administered to a patient, what would be the concentration of the medication in 12 hours? b. C. Suppose the medication was administered 24 hours ago. If the concentration in the bloodstream is now 2 mg/ml, what was the initial dose? What does the function C(t) imply about the half-life of this particular medication? That is, how long will it take for the concentration of the drug to be cut in half?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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300 ernet and after only 5 days each person only had to pay e registered to donate in 5 days? 310 3 P pn рци ad re 0.50x = 360 d. a. b. преора d. مساه 3. A certain type of bacteria cell quadruples two times an hour when exposed to heat. Suppose a petri dish contains 10 of these bacteria cells. A lab technician places the petri dish on a plate warmer and observes the change in cells over time. What is the yearly average percentage rate for the investment account? Assuming there are no other deposits or withdrawals, what is the balance in the account after 25 years? Write an equation to model the bacteria growth. Be sure to label the variables. How many cells are in the petri dish after 3 hours? What is the average rate at which the bacteria cells increase each hour? n be ma
Transcribed Image Text:300 ernet and after only 5 days each person only had to pay e registered to donate in 5 days? 310 3 P pn рци ad re 0.50x = 360 d. a. b. преора d. مساه 3. A certain type of bacteria cell quadruples two times an hour when exposed to heat. Suppose a petri dish contains 10 of these bacteria cells. A lab technician places the petri dish on a plate warmer and observes the change in cells over time. What is the yearly average percentage rate for the investment account? Assuming there are no other deposits or withdrawals, what is the balance in the account after 25 years? Write an equation to model the bacteria growth. Be sure to label the variables. How many cells are in the petri dish after 3 hours? What is the average rate at which the bacteria cells increase each hour? n be ma
2. 1. By the day of the event. enou F a. ^ Applications of Exponential Functions of the Form y = ab* The half-life of a drug is an estimate of the period of time it takes for the concentration of the drug in the body to be reduced by exactly one half. a. 0.50=366 x b. 0.50x=360 C. x=720 peop Suppose the concentration C in mg/ml of a certain medication in terms of its half- life can be modeled by the function Tania Rachel Alvarengu 3124 3A C (t) = A ( ² ) where A represents the initial dose of the medication in mg and t represents the number of hours since the initial dose. If 20 mg of the medication was initially administered to a patient, what would be the concentration of the medication in 12 hours? Suppose the medication was administered 24 hours ago. If the concentration in the bloodstream is now 2 mg/ml, what was the initial dose? The amount of money A in an investment account over time t in years can be modeled by the function below: What does the function C(t) imply about the half-life of this particular medication? That is, how long will it take for the concentration of the drug to be cut in half? t A(t) = 1500(2) 10 Interpret the quantity 1500 in the context of the problem. 7 t b. Interpret the quantity (2) in the context of the problem. In Maryl he i OF C
Transcribed Image Text:2. 1. By the day of the event. enou F a. ^ Applications of Exponential Functions of the Form y = ab* The half-life of a drug is an estimate of the period of time it takes for the concentration of the drug in the body to be reduced by exactly one half. a. 0.50=366 x b. 0.50x=360 C. x=720 peop Suppose the concentration C in mg/ml of a certain medication in terms of its half- life can be modeled by the function Tania Rachel Alvarengu 3124 3A C (t) = A ( ² ) where A represents the initial dose of the medication in mg and t represents the number of hours since the initial dose. If 20 mg of the medication was initially administered to a patient, what would be the concentration of the medication in 12 hours? Suppose the medication was administered 24 hours ago. If the concentration in the bloodstream is now 2 mg/ml, what was the initial dose? The amount of money A in an investment account over time t in years can be modeled by the function below: What does the function C(t) imply about the half-life of this particular medication? That is, how long will it take for the concentration of the drug to be cut in half? t A(t) = 1500(2) 10 Interpret the quantity 1500 in the context of the problem. 7 t b. Interpret the quantity (2) in the context of the problem. In Maryl he i OF C
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