The reaction of chemical compounds can often be modeled by differential equations. Let y(t) be the concentration of a substance in reaction for t ≥ 0 (typical units of y are moles/L). The change in the concentration of the substance, under appropriate conditions, is 

dy/dt = -kyⁿ, where k > 0 is a rate constant and the positive integer n is the order of the reaction. 

a. Show that for a first-order reaction (n = 1), the concentration obeys an exponential decay law.

b. Solve the initial value problem for a second-order reaction (n = 2) assuming y(0) = y₀.

c. Graph and compare the concentration for a first-order and second-order reaction with k = 0.1 and y₀ = 1.