Question

# Decide if the equation represents exponential growth or decay. Explain your answer. y=((3^x)/(2^x))

Exponential growth and decay
Decide if the equation represents exponential growth or decay. Explain your answer. $$\displaystyle{y}={\left(\frac{{{3}^{{x}}}}{{{2}^{{x}}}}\right)}$$
An equation of the form $$\displaystyle{y}={a}\cdot{b}^{{x}}$$ represent exponential growth when b>1 and represents exponential decay when b
$$\displaystyle{y}={\left(\frac{{{3}^{{x}}}}{{{2}^{{x}}}}\right)}={\left(\frac{{3}}{{2}}\right)}^{{x}}$$
Since $$\displaystyle\frac{{3}}{{2}}{>}{1},{y}={\left(\frac{{{3}^{{x}}}}{{{2}^{{x}}}}\right)}={\left(\frac{{3}}{{2}}\right)}^{{x}}$$ represent exponential growth.