Exponential and Logistic Modeling on a Graphing Calculator
Key Questions

I don't think you can make a model with the
#e# or the two#k# and the#t# . However, you can make a#y=ab^x# model using the Exponential Regression key. To use this, go to STAT#># CALC#># and scroll down until you see "ExpReg".Then, if you have data entered into your STAT key, then you'll get a model for that.
Hope that helps :)

I assume you mean the "A" as in the initial value of
#y=Ae^(rt)# ?#y# interceptThe "a" value occurs at
#t=0# , so#e^0=1# , therefore#y=A# is#(0,A)# , the#y# intercept. 
Consider the exponential function
#f(x)=a^(kx)# , where#a# and#k# are constant,#a, k in RR# .I prepared a dynamic plot that can be used to study the properties of the exponential function as
#a# and#k# take various values.Please use the provided sliders to change the values of the parameters
#a# and#k# and see what happens to the graph of the function.Pay particular attention to the cases when
# 0 < a < 1 # and# a > 1# . For each of these cases, see what happens when#k<0# and#k>0# . 
Answer:
See the video from YouTube.
Explanation:
The following steps shown on the TI84 is the same as the steps found on a TI83.