Find C and a so that f(x) = Ca^x satisfies the given conditions. f(-2) = 4/3, f(2) = 1/12

Answer 1

f(x) = Ca^x

Since f(-2) = 4/3, Ca^-2 = 4/3. So, C = (4/3)a².

Since f(2) = 1/12, Ca² = 1/12.

So, (4/3)a⁴ = 1/12.

a⁴ = 1/16

a = 1/2 and C = (4/3)(1/2)² = 1/3

Therefore, f(x) = (1/3)(1/2)^x