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anonymous
 5 years ago
The quantity of a drug in the bloodsteam t hours after a tablet is swallowed is given, in mg, by q(t)=40((e^t)(e^2t))
What is the maximum amount of the drug in the bloodstream at one time?
anonymous
 5 years ago
The quantity of a drug in the bloodsteam t hours after a tablet is swallowed is given, in mg, by q(t)=40((e^t)(e^2t)) What is the maximum amount of the drug in the bloodstream at one time?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the maximum is at \[q \prime (t)=0 \implies 40(e ^{t}+2e ^{2t})=0 \implies 2e ^{2t}=e^t\] take ln for both sides, you get \[\ln(2e ^{2t})=\ln(e ^{t}) \implies \ln22t=t \implies t=\ln2\] t=ln2 is the only critical point..substitute in the original function with t=ln2, you get: q(ln2)=40(1/2  1/4)=10 mg
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