Exponential Growth and Decay. Applications and Models

All of the examples for Exponential growth and decay in 10.4 were great, but the one I had difficulty with was Continuously compounded interest. I understand that dB/dt is the rate (0.05) times the amount in the savings account, but the book says the intial amount of $1000 doesn't matter? why though, since the amount in the account would be the initial $1000. Why does the ODE not need the initial value? What is confusing is that in the solution of the ODE they do use the initial $1000 as B(sub0). Could you explain initial values and their involvement with ODE in class?

What I really enjoyed were all the applications of ODE's in section 10.5. I felt as if the book used an example from every possible situation so that every one could relate to at least one example. Similar to how economic examples will confuse me to no end, there is opportunity in drug quantity problems or physics (Newton's Law)!

I think that the only confusing situation that the class may have trouble with is the equilibrium solutions. It begins like a drug elimination ODE but the idea of stability/instability depending on if the reaction goes to infinity needs clarification. I personally have worked with biological and chemistry equilibriums and I have never come across equilibriums in math before.

By the way Chad... Amazing job on your swarming presentation, it was really interesting. I must admit though I chuckled when I saw a differential equation on the power point!