Find C and a so that f(x) = Ca^x satisfies the given conditions. f(1) = 81, f(2) = 729

Answer 1

Just plug in the points for x and y from the points (1, 81) and (2, 729)

y = Ca^x

1) 81 = Ca¹ or C = 81/a

2) 729 = Ca² plugging in "81/a" for "C" we get 729 = (81/a)a² or 729 = 81a or a = 9

Plugging in "9" into C = 81/a we get C = 9

So a = 9 and C = 9

f(x) = 9*9^x