1.5 and 1.7

Blog for reading due Tuesday 9/2, on 1.5 and 1.7

1) Main Points:

Whenever you have a constant percent increase it's exponential growth. If the rate of change number is greater than zero and less than one the function is a decreasing exponential function. Growth and decay can be modeled by P=P(e) to the (k x t) power. Every exponentially growing function has a fixed doubling time. For interest: annually P=P(1+r) to the t, continuously P=Pert. B, the future value of a payment is the amount P would have grown if in an interest-bearing bank account.

2) Challenges:

I was challenged by the example given of a decreasing exponential function. For something that is decreased by 40% for every
unit of time, it took me a while to understand that 60% of it would be left each time. Another confusing aspect of exponential functions is that the absolute rate of change is not constant but the relative rate of change is. For solving exponential growth and decay problems I will have to remember to use natural log, Ln, to isolate the variable. It took me a while to understand the two ways of calculating the future values of sums of money (re: interest), you can either calculate what the actual present value of it is or you can calculate what it will be worth in the future.

3) Reflections:

Exponential functions apply very well to population data, because most often populations grow faster as they get bigger. I also notice this mathematical relationship in cells reproduction. Future and Present values were concepts that were new to me but they show many practical uses for determining not only the changing value of money but of other things in nature the exhibit predictable change.