The concentration of the active ingrediaent in a chemical usedto control insects

Question

The concentration of the active ingrediaent in a chemical usedto control insects decays exponentially with time. Twelvehours after application, 50% of the active ingredient decays. Whatpercent of active ingredient decays after 36 hours? I don't even know where to start... The concentration of the active ingrediaent in a chemical usedto control insects decays exponentially with time. Twelvehours after application, 50% of the active ingredient decays. Whatpercent of active ingredient decays after 36 hours? I don't even know where to start...

Explanation / Answer

New amount = initial amount times e to the power rate of decaytimes time A= Ao ert If 50% of the active ingredient is gone after 12 hours we cansolve for r: If you begin with 1000 grams and 50% goes away then you areleft with a final amt =500 500=1000 e r(12)divide both sides of equation by1000 .5 = e 12r     take the LN ofboth sides of equation LN .5 = LN e12r     do LN .5 oncalculator; the LN e12r  is 12 r becauseLN=loge so loge e 12r is asking "whatexponent do you put on base e to gete12r?" answer 12r LN .5 = LN e12r    -.6931 = 12r     divide both sides ofequation by 12 -.1578 = r You use the above answer to solve the next part of theproblem: A= Ao e-.1578 t    t=36hours; let Ao = 1000 grams A= 1000 e-.1578(36)   t=36 hours A=1000(.125) A=125 grams You started with 1000 grams and ended upwith 125 so to find the percent left you change 125/1000 to apercent = 12.5%

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