Section 3.1

I finished most of the assigned homework problems for section 3.1 (intro to the family of exponential functions). The main points in this section are about the exponential formula: f(t)= ab^t, b>0.

What's really important in the equation is that 'a' is the initial value of Q (at t=0) and b, the base, is the GROWTH FACTOR (b>1 gives exponential growth and 0 'r' is the "decimal representation of the percent rate of change"... meaning that 'r' is the percent given in the problem if it says something like Tom's salary grew 20% per year. 20% (or .20) is 'r'. Then to figure out 'b' so you can figure out an equation, you need to plug in 'r' into (1+r) = b. so... 1+.2 = 1.2 = b... then plug that into the equation of the function and you have f(t)= a(1.2)^t! And 'a' is the initial value.. so let's say Tom's salary starts at $1,000/year, so then plug that into the equation as well and you have:

Q=f(t)=1000(1.2)^t (t is in years)

Even though I understood all of this, I had some trouble on questions: 25d and all of 31. I'll ask my teacher about those soon. But I get the overall feel of this section.

Now on to section 3.2: Comparing exponential and linear functions!