Finding the explicit rule for an exponential equation is easy if you know two things… The begining quantity at F(0) and the ratio of growth (growth factor).
Ex. 1. The 1’t term F(1) is 4 the second term F(2) is 8 the third term F(3) is 16. Each successive term is twice the previous. Thus the growth factor or ratio is 2. If we work backward from the 1’st term which is 4 and find the previous term F(0) which is half that or 2, you have all you need to write an explicit rule.
F(x) = F(0)(ratio)raised to the power of the term you want
F(x) = (2)(2 raised to the power of the term you want)
So if you want to find the 4’th term….
F(4) = (2)(2 to the 4’th) or (2)(16) = 32
