Find a formula for the exponential function that satisfies g(0)=5 and g(−2)=5/2.

Answer 1

g(x) = A(B)^x

Since g(0) = 5, A(B)⁰ = 5. So, A = 5.

g(x) = 5(B)^x

Since g(-2) = 5/2, 5(B)^-2 = 5/2

B^-2 = 1/2

B² = 2 So, B = √2

g(x) = 5(√2)^x