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her first day in a hospital, Kiri receives u₁ milligrams (mg) of a therapeutic drug. The amount of the drug Kiri receives increases by the same amount, d, each day. On the seventh day, she receives 21 mg of the drug, and on the eleventh day she receives 29 mg. Kiri receives the drug for 20 days. Ted is also in a hospital and on his first day he receives a 20 mg antibiotic injection. The amount of the antibiotic Ted receives decreases by 50% each day. On the second day, Ted receives a 10 mg antibiotic injection, on the third day he receives 5mg, and so on.

her first day in a hospital, Kiri receives u₁ milligrams (mg) of a therapeutic drug. The amount of the drug Kiri receives increases by the same amount, d, each day. On the seventh day, she receives 21 mg of the drug, and on the eleventh day she receives 29 mg. Kiri receives the drug for 20 days. Ted is also in a hospital and on his first day he receives a 20 mg antibiotic injection. The amount of the antibiotic Ted receives decreases by 50% each day. On the second day, Ted receives a 10 mg antibiotic injection, on the third day he receives 5mg, and so on.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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1) On her first day in a hospital, Kiri receives u₁ milligrams (mg) of a therapeutic drug. The amount of the drug Kiri receives increases by the same amount, d, each day. On the seventh day, she receives 21 mg of the drug, and on the eleventh day she receives 29 mg. Kiri receives the drug for 20 days. Ted is also in a hospital and on his first day he receives a 20 mg antibiotic injection. The amount of the antibiotic Ted receives decreases by 50% each day. On the second day, Ted receives a 10 mg antibiotic injection, on the third day he receives 5mg, and so on. a) i) Write down an equation, in terms of u₁ and d, for the amount of the drug that she receives on the seventh day. ii) Write down an equation, in terms of u₁ and d, for the amount of the drug that she receives on the eleventh day. b) Write down the value of d and the value of u₁. c) Calculate the total amount of the drug, in mg, that she receives. d) i) Find the amount of antibiotic, in mg, that Ted receives on the fifth day. ii) The daily amount of antibiotic Ted receives will first be less than 0.06 mg on the kth day. Find the value of k. iii) Hence find the total amount of antibiotic, in mg, that Ted receives during the first k days.
Transcribed Image Text:1) On her first day in a hospital, Kiri receives u₁ milligrams (mg) of a therapeutic drug. The amount of the drug Kiri receives increases by the same amount, d, each day. On the seventh day, she receives 21 mg of the drug, and on the eleventh day she receives 29 mg. Kiri receives the drug for 20 days. Ted is also in a hospital and on his first day he receives a 20 mg antibiotic injection. The amount of the antibiotic Ted receives decreases by 50% each day. On the second day, Ted receives a 10 mg antibiotic injection, on the third day he receives 5mg, and so on. a) i) Write down an equation, in terms of u₁ and d, for the amount of the drug that she receives on the seventh day. ii) Write down an equation, in terms of u₁ and d, for the amount of the drug that she receives on the eleventh day. b) Write down the value of d and the value of u₁. c) Calculate the total amount of the drug, in mg, that she receives. d) i) Find the amount of antibiotic, in mg, that Ted receives on the fifth day. ii) The daily amount of antibiotic Ted receives will first be less than 0.06 mg on the kth day. Find the value of k. iii) Hence find the total amount of antibiotic, in mg, that Ted receives during the first k days.
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