<ol class="i-list"><li><div class="list-item-paragraph">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.</div></li><li><div class="list-item-paragraph">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</div><div class="list-item-paragraph" style="text-align: center">${{x}_{n+1}}=50+{{\left( 0.88 \right)}^{6}}{{x}_{n}}$,</div><div class="list-item-paragraph">where&nbsp;${{{x}_{n}}}$ denotes the number of units of antibiotic in the body after the ${n^{\mathrm{th}}}$ pill is taken.</div><ol class="abc-list"><li><div class="list-item-paragraph">As&nbsp;$n\to \infty $, ${{x}_{n}}\to $${L}$. Determine the value of ${L}$.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Show that&nbsp;${{x}_{n+1}}&gt;{{x}_{n}}$ if&nbsp;${{x}_{n}}L$ .<span class="inline-marks">[3]</span></div></li></ol></li></ol>

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.

where ${{{x}_{n}}}$ denotes the number of units of antibiotic in the body after the nth pill is taken.

As $n\to \infty $, ${{x}_{n}}\to $${L}$. Determine the value of ${L}$.

Show that ${{x}_{n+1}}>{{x}_{n}}$ if ${{x}_{n}}L$ .

Recurrence Relations and Summation

H2 Math

International Baccalaureate Higher Level Mathematics

2012 VJC P1 Q5

2012 VJC P1 Q5

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