3. Given : \( g(x)=k^{x} \) find \( k \), if \( g \) passes through \( (5 ; 32) \)

To find \( k \) in the function \( g(x) = k^x \) that passes through the point \( (5, 32) \), you plug in the coordinates into the equation. This gives you: \[ g(5) = k^5 = 32 \] Next, rewrite 32 as \( 2^5 \): \[ k^5 = 2^5 \] By equating the bases, you find that \( k = 2 \). So, the function is \( g(x) = 2^x \). Isn’t it fun how these mathematical relations lead us to uncover \( k \)? Now you have \( g(x) \) all set up!