10.4: Exponential Growth and Decay

Main Points
For the differential equation dy/dx = ky, its general solution is y = Ce^kt for any constant C. When k > 0 this is known to be exponential growth and when k < 0, this is exponential decay. y = C when t = 0. Exponential growth solution curves become exponential decay curves when they are reflected over the y axis. A differential equation is only an approximation of a representation of a number of values, but for large values this approximation method is pretty accurate.

Challenges
In example 1, I do not understand how the solution for iii was obtained. I'm not sure I understand how to set up a differential equation.