# Is the function  y = -5(1/3)^ -x exponential growth or decay?

You can answer the question by calculating the first derivative. First of all, applying the rule ${a}^{- x} = \frac{1}{{a}^{x}}$, we have that ${\left(\frac{1}{3}\right)}^{- x} = {3}^{x}$. Then, since you can factor out constants, you have that
$\frac{d}{\mathrm{dx}} - 5 {\left(\frac{1}{3}\right)}^{- x} = - 5 \setminus \frac{d}{\mathrm{dx}} {\left(\frac{1}{3}\right)}^{- x} = - 5 \setminus \frac{d}{\mathrm{dx}} {3}^{x}$
As a fundamental derivative, we know that $\frac{d}{\mathrm{dx}} {3}^{x} = {3}^{x} \cdot \log \left(3\right)$.
So, the first derivative is $- 5 \setminus \log \left(3\right) \cdot {3}^{x}$, which is always negative since $5 \setminus \log \left(3\right) \cdot {e}^{x}$ is always positive. So, your function is always decreasing, and you have exponential decay.