Answer
The function represents exponential growth and the rate of growth is $25\%$.
Work Step by Step
The given function is
$\Rightarrow g(t)=2(\frac{5}{4})^t$
$\Rightarrow g(t)=2(1.25)^t$
$\Rightarrow g(t)=2(1+0.25)^t$
The function is of the form
$y=a(1+r)^t$, where $1+r>1$.
So, it represents exponential growth.
Growth factor is
$\Rightarrow 1+r=1.25$
Subtract $1$ from each side.
$\Rightarrow 1+r-1=1.25-1$
Simplify.
$\Rightarrow r=0.25$
$\Rightarrow r=25\%$.
Hence, the function represents exponential growth and the rate of growth is $25\%$.
