Question

# Tell whether the function represents exponential growth or exponential decay. Explain your reasoning. y=(1/2)e^3x

Exponential growth and decay
Tell whether the function represents exponential growth or exponential decay. Explain your reasoning.
$$\displaystyle{y}={\left(\frac{{1}}{{2}}\right)}{e}^{{3}}{x}$$

2021-02-10
We are given the equation.
$$\displaystyle\frac{{1}}{{2}}$$ times $$\displaystyle{e}^{{3}}{x}$$
2Find the pieces of the function (a and r)
$$\displaystyle{a}=\frac{{1}}{{2}}$$
r = 3x
3Go by Natural Base Functions.
If a > 0 and r > 0, function is exponential growth function.
If a > 0 BUT r < 0, function is exponential DECAY function.