Find C and a so that f(x)=Ca^x satisfies f(-1)=2 and f(1)=18

Answer 1

Use the 2 given points to find C and a.

f(1) = 18 ⇒ Ca¹ = Ca = 18

f(-1) = 2 ⇒ C/a = 2

(Ca)(C/a) = C² = 18(2) = 36

C = 6

a = 18/C = 18/6 = 3

f(x) = 6 (3)^x

Test the answer.