\(\displaystyle{y}={a}{\left(\frac{{3}}{{2}}\right)}^{{t}}\)

This is a growth function

Rate of decay is 1.5-1=0.5

That is 50%

Consider an exponential function of the form: \(\displaystyle{y}={b}\cdot{a}^{{x}}\)

If a>1, then it is exponential growth function with growth rate a-1

If a<1, then it is exponential decay function with decay rate 1-a

This is a growth function

Rate of decay is 1.5-1=0.5

That is 50%

Consider an exponential function of the form: \(\displaystyle{y}={b}\cdot{a}^{{x}}\)

If a>1, then it is exponential growth function with growth rate a-1

If a<1, then it is exponential decay function with decay rate 1-a