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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Exponential growth occurs when a quantity increases by the same factor over equal intervals of time. This leads to an exponential function, where the independent variable in the exponent, $t,$ is time.
$y=a⋅b_{t}$
Since the quantity **increases** over time, the constant multiplier $b$ has to be **greater** than $1.$ Thus, $b$ can be split into two terms, $1$ and $r,$ where $r$ is some positive number. The resulting function is called an *exponential growth function*.

The constant $r$ can then be interpreted as the *rate of growth*, in decimal form. A value of $0.06,$ for instance, means that the quantity increases by $6%$ over every unit of time. As is the case with all exponential functions, $a$ is the $y$-coordinate of the $y$-intercept. The base of the power, $1+r,$ is known as the *growth factor*, and since it's greater than $1$ the quantity grows faster and faster, without bound.