Asked by Anonymous
The blood alcohol concentration after a drink has been consumed can be modelled by c(t)=(0.02t)e^(−0.05t) where t is the time in minutes elapsed after the consumption of the drink and c(t) is the concentration in mg/mL at t. At what time in the first hour after consuming the drink is the blood alcohol concentration the highest?
I was assuming that u could set c(t)=0 to solve for t but I don't think that will work.
I was assuming that u could set c(t)=0 to solve for t but I don't think that will work.
Answers
Answered by
Steve
Of course it will work. Since you're learning about using derivatives to locate extrema, why would you think it would not work?
dc/dt = (0.02t - 0.001) e^(-0.05t)
since e^(-0.05t) is never zero, you want
0.02t - 0.001 = 0
dc/dt = (0.02t - 0.001) e^(-0.05t)
since e^(-0.05t) is never zero, you want
0.02t - 0.001 = 0
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