A hospital patient is given a pill containing ${50}$ units of antibiotic at 12pm. By 1pm, the numb

Question

A hospital patient is given a pill containing ${50}$ units of antibiotic at 12pm. By 1pm, the number of units of antibiotic in the patient’s body has dropped by ${12\%}$. By 2pm, a further ${12\%}$ of the antibiotic remaining in the blood at 1pm is lost. Given that the rate of decrease is such that the amount of antibiotic drops by ${12\%}$ every one hour, find the amount of antibiotic remaining in the blood at 6pm. A doctor considers prescribing a course of treatment which involves the patient taking the pill every ${6}$ hours over a long period of time. It is given that ${{x}_{n+1}}=50+{{\left( 0.88 \right)}^{6}}{{x}_{n}}$, where ${{{x}_{n}}}$ denotes the number of units of antibiotic in the body after the ${n^{\mathrm{th}}}$ pill is taken. As $n\to \infty $, ${{x}_{n}}\to $${L}$. Determine the value of ${L}$.[2] Show that ${{x}_{n+1}}>{{x}_{n}}$ if ${{x}_{n}}L$ .[3]

Accepted Answer

(i) $23.2$ units (ii) (a) $L=93.4$

2012 VJC P1 Q5

2012 VJC P1 Q5

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