# How do you determine if the equation y = 3(0.4)^x represents exponential growth or decay?

Jul 17, 2016

#### Explanation:

Take a look at the equation: $y = a \cdot {b}^{x}$

When $b > 1$, the equation represents exponential growth. When $b$ is between $0$ and $1$, the equation represents exponential decay.

The equation $y = 3 {\left(0.4\right)}^{x}$ represents exponential decay, since $b$, or $0.4$, is greater than $0$ and less than $1$.

Look at the graph to confirm exponential decay.
graph{3(0.4)^x [-6.71, 13.29, -2.17, 8.25]}

Jul 17, 2016

The eqn. represents decay.

#### Explanation:

We know that, the function ${a}^{x}$ is $\uparrow$ for $a > 1$ and it is $\downarrow$ for $0 < , a < , 1$

$\therefore {\left(0.4\right)}^{x}$ is $\downarrow$ & so is $y = 3 {\left(0.4\right)}^{x}$

Therefore, the eqn. represents decay.