Given the following equation of an exponential function determine the base, b, of the exponential model. Is the base a growth or decay factor? a. b is 0.6394; It is a growth factor. b. b is 0.6394; It is a decay factor. c. b is 20.5; It is a growth factor. d. b is 20.5; It is a decay factor.  

B. b is 0.6394; It is a decay factor.
   Thank you for including the equation N=20.5(0.6394)^t. That equation is vital. Now let's look at the 3 parts and see what each does. 20.5; This is merely a constant scaling factor. So we can ignore this value. 0.6394; This is the base for the exponential function. t; This is the power to raise the base to. So now the question becomes one of is that base a growth, or decay factor. Since it's value is less than 1, it is a decay factor. For example, take 0.9 and look at the various powers. 0.9^0 = 1 0.9^1 = 0.9 0.9^2 = 0.81 As you can see, each successive term is smaller. And that behavior will happen for ANY base that has a value less than 1. If the base is greater than 1, then it will be a growth factor since each successive term will be larger than the previous. So the answer is option "B" which both correctly identifies the base as 0.6394 and the fact that it's a decay factor.