Please help, thank you!
1. a colony of bacteria in a culture grows at a rate given by N(t)=2^(t/5) where N is the number of bacteria t minutes from the beginning. The colony is allowed to grow for 60 mins at which time a drug is introduced to kill the bacteria. The number of bacteria killed is given by K(t)=e^(t/3) where K bacteria are killed at time t minutes.
a) determine the max number of bacteria present and the time at which this occurs.
b) determine the time at which the bacteria colony is obliterated.
2. Loraine is studying for 2 different exams. Because of the nature of the courses, the measure of study effectiveness on a scale from 0 to 10 for the first course is E1 = 0.6(9 + te^-t/20), while the measure for the 2nd course is E2=0.5(10 + te^-t/10). Loraine is prepared to spend up to 30 hours in total studying. THe total effectiveness is given by f(t)=E1+E2. How should this time be allotted to maximize total effectiveness?