# What is the y-intercept of all exponential growth functions?

May 28, 2018

$\left(0 , 1\right)$

#### Explanation:

the general formula for any exponential function is ${a}^{x}$.

(e.g. ${2}^{x} , {3}^{x}$)

the $y$-intercept of a graph is the point where it touches the $y$-axis. the $y$-axis touches the $x$-axis when $x = 0$.

the $y$-intercept of the graph is the point where $x = 0$ and $y$ is a certain value.

if the exponential function is ${a}^{x}$, then the $y$-intercept is the point where ${a}^{x} = {a}^{0}$.

any number raised to the power of $0$ gives $1$.

hence ${a}^{0}$ will always be $1$.
is $y = {a}^{x}$, then the $y$-intercept is $\left(0 , {a}^{0}\right)$, which is $\left(0 , 1\right)$.