a pair of points on the graph of an exponential function is given. find a formula for the function.

So we have

40 = ab⁸  and 8 = ab⁴⁰

Using the first, we can solve for a  =   40/b⁸ ........and substituting this into the second, we have

8 =(40/b⁸)b⁴⁰  

8 = 40b³²        divide both sides by 8

(1/5) = .20 = b³²            take the (positive) 32nd root of both sides

b = about .951

And substituting this into 40 = ab⁸  to find a, we have

40 = a(.951)⁸        divide both sides by (.951)⁸ 

a = 40 / (.951)⁸  = about 59.79

So....our function is

w(x) = 59.79(.951)^x