Find the exponential function f ( x ) = a ^x that passes through the point ( − 2 , 25 ) and has a y-intercept of 1.

Answer 1

f(x) = a^x

Since f(-2) = 25, a^-2 = 25.

1/a² = 25 So, a² = 1/25. Therefore, a = 1/5

f(x) = (1/5)^x Note: f(0) = (1/5)⁰ = 1. So, the y-intercept is 1.