Answer
The function represents exponential growth and the rate of growth is $25\%$.
Work Step by Step
The given function is
$\Rightarrow f(t)=4(1.25)^{t+3}$
Use $(a)^{m+n}=a^m\cdot a^n$.
$\Rightarrow f(t)=4(1.25)^{t}(1.25)^{3}$
$\Rightarrow f(t)=4(1.25)^{3}(1.25)^{t}$
$\Rightarrow f(t)=4(1.25)^{3}(1+0.25)^{t}$
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 an exponential growth and the rate of growth is $25\%$.
