SOLUTION: The half-life of caffeine is 5 hours. This means the amount of caffeine in your bloodstream is reduced by 50% every 5 hours. A grande French Roast has 330 milligrams of caffeine. L

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Question 720804: The half-life of caffeine is 5 hours. This means the amount of caffeine in your bloodstream is reduced by 50% every 5 hours. A grande French Roast has 330 milligrams of caffeine. Let Q(t) denote the amouunt of caffeine in your system T hours after consuming your grande French Roast. For simplicity, assume the entire grande French Roast is consumed instantly.
A.) How many milligrams of caffeine will be in your systemafter 5 hours? After 10 hours? After 15 hours? (THINK! THIS PART SHOULD NOT REQUIRE A LOT OF WORK.)
B.) Q(t)=Q[subgrade cero 0]E^-kt .... FIND Q[subgrade cero], if k=4.
c.) How many milligrams of caffeine will be in your system after 2 hours if k=2?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Question #A is very simple as you say. Question #B requires a little more care. You wanted, k=4. Why? I would not first use k=4 unless directions specify to do so. You were given a half-life for the caffeine. Why not use the Q(t) equation for decay to solve for k using the given half life? What is the actual question to be answered in #B? Find t? Find Q%5B0%5D which was already given? No time was given? 330 mg. as given, of caffeine. The situation described seems to indicate Q%28t%29=330%2Ae%5E%28-k%2At%29, but you are saying to use k=4. If this were correct, then you might want to say, Q%28t%29=330%2Ae%5E%28-4%2At%29. THOSE DO NOT SEEM RIGHT.

Making more sense should be, use half life to find k.
%281%2F2%29Q=Qe%5E%28-k%2A5%29
%281%2F2%29=e%5E%28-k%2A5%29
ln%281%2F2%29=-5k%2A1
k=-%281%2F5%29ln%281%2F2%29
k=%281%2F5%29%280.693%29
highlight%28k=0.139%29

Not sure for #B, but a better way to handle #C would be use the equation, Q%28t%29=330e%5E%28-0.139%2At%29 for t=2 hours. Any such values k=2 or k=4 do not make sense.