document.write( "Question 1070768: The delivery of a drug (such as an antibiotic) through an intravenous line may be modeled by the differential equation m'(t) + km(t) = I, where m(t) is the mass of the drug in the blood at time t ≥0, k is a constant that describes the rate at which the drug is absorbed, and I is the infusion rate. Let I =15 mg/hr and k = 0.5 hr-1 . For what initial values m(0) = A are solutions increasing? decreasing? What is the equilibrium solution? \n" ); document.write( "

Algebra.Com's Answer #685784 by Fombitz(32388) $\"\"$ $\"About$

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$\"dm%2Fdt%2B0.5m=15\"$
\n" ); document.write( " $\"m=Ce%5E%28-0.5t%29%2B15%2F0.5\"$
\n" ); document.write( " $\"m=Ce%5E%28-0.5t%29%2B30\"$
\n" ); document.write( "So when $\"t=0\"$ ,
\n" ); document.write( " $\"C%2B30=A\"$
\n" ); document.write( " $\"C=A-30\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"m%28t%29=%28A-30%29e%5E%28-0.5t%29%2B30\"$
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\n" ); document.write( "So depending on the value of A the function is either increasing or decreasing.\r
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\n" ); document.write( "Decreasing if $\"A%3E30\"$
\n" ); document.write( "Increasing if $\"A%3C30\"$
\n" ); document.write( "Constant if $\"A=30\"$
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\n" ); document.write( "As t gets large, $\"m%28t%29=30\"$
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