Write the exponential equation with horizontal asymptote \(y~=~0\), \(y\text{-}\text{intercept}\) \(5\), and growth factor \(2\).

Use the form with an initial scale, a repeated factor, and a vertical shift. The horizontal asymptote determines the shift, the stated growth factor becomes the base, and substituting input zero turns the intercept into the initial scale because the exponential factor becomes one. Verify each role separately so the intercept and growth factor are not accidentally swapped.