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.
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