Exponential graphs

An exponential function has the form $y = a \cdot b^x$, where $a$ is the starting value and $b$ the multiplier applied each step. Its graph curves rather than bending at a point.

When $b > 1$ the function grows and the curve rises ever more steeply. When $0 < b < 1$ it decays and the curve falls toward the axis. Both pass through $(0, a)$, because anything to the power zero is $1$.

The flat line the curve approaches is the asymptote. For $y = a \cdot b^x$ it is $y = 0$, and the curve gets arbitrarily close without ever touching it. Adding a constant shifts the asymptote: $y = 2^x + 3$ approaches $y = 3$.

The difference from a line is worth stating plainly. A linear function adds the same amount each step; an exponential multiplies by the same factor. That is why exponential growth eventually overtakes any linear growth, however steep the line.

What is the $y$-intercept of $y = 5 \cdot 3^x$?
Set $x = 0$, and since $3^0 = 1$