10.4 & 10.5 Exponential growth and decay & Applications and modeling

Main points:
• General solution to dy/dt=ky is y=Ce^kt for any constant C
○ Exponential growth for k>0
○ Exponential decay for k<0
○ The constant C is the value of y when t is 0
• General solution to dy/dt=k(y-A) is y=A+Ce^kt for any constant C
○ Arbitrary constant C is the initial value of y-A
• An equilibrium solution
○ Constant for all values of the independent variable. The graph is a horizontal line.
○ Stable if a small change in the initial conditions gives a solution which tends toward the equilibrium as the independent variable tends to positive infinity
○ Unstable if a small change in the initial conditions gives a solution a curve which veers away from the equilibrium as the independent variable tends to positive infinity

Challenges:
I did understand the general concepts, but I still have problems applying them to real problems. Especially translating the problems to mathematics was something that I found difficult. I had problems understanding the example of Pollution in Great Lakes, so I would appreciate if we could go through it in class.

Reflection:
Today was difficult because I was really tired so I kept reading the sentences several times in order to understand them. Shows that I really need to consider whether it is worth trying to study if I am just very exhausted. I liked the examples on continuously compounded interest and company's revenue as the relate to economics.