1. A population of bacteria grows at rate N'(t) = 20e0.05t after t hours, under ideal conditions. There are initially 10 bacteria present.
(a) Find N(t) for t ≥ 0.
(b) How many hours does it take for the population to reach 1 million?
2. Suppose the acceleration of an object traveling in one-dimension is given by a(t) = -4 m/s2. Assuming the object was initially traveling at 150 m/s and s(0) = 0, find the velocity function v(t) and the position function s(t) for t ≥ 0.