# How do you identify equations as exponential growth, exponential decay, linear growth or linear decay f(x) = 9.6 ∙ 1.06x?

Oct 7, 2015

See explanation below.

#### Explanation:

A linear expression has a form of $f \left(x\right) = a x + b$. It is an increasing function ("growth" as you call it) if $a > 0$, if $a < 0$ then it is a decreasing function ("decay")

An exponential function has a form of $f \left(x\right) = a \cdot {b}^{x}$, it is usually defined for $b > 0$. Such a function is growth if $a > 1$ or decay if a in (0;1).

So if you meant to write $f \left(x\right) = 9.6 \cdot 1.06 x$, then it is a linear growth function.

But if you mean a function like:

$f \left(x\right) = 9.6 \cdot {\left(1.06\right)}^{x}$,

then it is an exponential function, and it is a growth ftnction, because $1.06 > 1$