"A 0.6ml dose of a drug is injected into a patient steadily forhalf a second. At the end of this time, the quantity, Q, ofthe drug in the body starts to decay exponentially at a continuousrate of 0.2% per second. Using formulas, express Q as acontinuous function of time, t in seconds."

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&quot;A 0.6ml dose of a drug is injected into a patient steadily forhalf a second. At the end of this time, the quantity, Q, ofthe drug in the body starts to decay exponentially at a continuousrate of 0.2% per second. Using formulas, express Q as acontinuous function of time, t in seconds.&quot;

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Question: &quot;A 0.6ml dose of a drug is injected into a patient steadily for half a second. At the end of this time, the quantity, Q, of the drug in the body starts to decay exponentially at a continuous rate of 0.2% per second. Using formulas, express Q as a continuous function of time, t inseconds.&quot; 1.PIECEWISE FUNCTION IS NEEDED BECAUSE WHAT HAPPENS DURINGINJECTION OF DRUG IS TOTALLY DIFFERENT FROM WHAT HAPPENS WHEN ITDECAYS. FIRST MAKE A TABLE LIKE THIS T..............Q..................RATE 0...............0.............. 0.5...........0.6...........DURING INJECTION =0.6/0.5=1.2ML/SEC...HENCE ---------------------Q=1.2T DURING T=0 TO 0.5 SEC. ------------- SUBSEQUENT TIME...THAT IS FORT&amp;gt;0.5 .............=AEB(T−0.5).....SINCE T IS TIME FROM BEGINING ANDDECAY STARTS AFTER INJECTION ..THAT IS AFTER 0.5 SECS ANDEXPONENTIAL FUNCION HOLDS IN THAT PERIOD ,WE PUT (T-0.5) NOW FOR A START AT T=0.5...Q=0.6...HENCE Q=AEB(0.5−0.5)=A=0.6...GOT IT.... NOW USE THE OTHER DATA OF 0.2%/SEC TO FIND B..HOPE YOU CAN CONTINUEWITH THIS APPROACH DQ/DT IS RATE OF DECAY....100*(DQ/DT)/Q IS % RATE OF DECAY.

"A 0.6ml dose of a drug is injected into a patient steadily forhalf a second. At the end of this time, the quantity, Q, ofthe drug in the body starts to decay exponentially at a continuousrate of 0.2% per second. Using formulas, express Q as acontinuous function of time, t in seconds."

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