Exponential functions 1.5 & 1.7

Main points:
• Exponential functions are expressed as f(x)=a^x. a is called the base or growth factor.
• P is exponential function of t with base a if P=Poa^t.
• Exponential growth/decay occurs when there is constant percentage change. When a>1 there is exponential growth and when 0 • e equals 2.71828... and is called natural base. Many quantities in nature change according to P=Poe^kt where P0 is the initial quantity and kt is the continuous growth/decay rate.
Challenges:I find it hard to put the mathematical concepts to my own words as English is not my first language. At the moment I do not have confidence with logarithms so I have to revise them too before I can fully approach exponential functions. Especially as e is often used with logarithms (or at least that is what I remember). I still did not fully understand why the factor a=1+r and I am looking forward to learn it in tomorrow's class. I am also looking forward to learn more about the natural base e and its importance, because in the past I have been bit intimidated by it.

Reflection: I found the topic useful through the examples of population growth and compound interest examples. The financial applications are something what I can use to my advantage in my own life.  I was also reminded that the functions can be solved in several ways, as in the past I was not so confident with formulas I used graphs instead. I have studied this in the past but found it too be more difficult than some other topics that I have managed to revise so far. I am looking forward to learn more about the natural base e and financial applications tomorrow.