Answer
The function represents exponential growth and the rate of growth is $6\%$.
Work Step by Step
The given function is
$\Rightarrow r(t)=0.4(1.06)^t$
$\Rightarrow r(t)=0.4(1+0.06)^t$
The function is of the form
$y=a(1+r)^t$, where $1+r>1$.
So, it represents exponential growth.
Growth factor is
$\Rightarrow 1+r=1.06$
Subtract $1$ from each side.
$\Rightarrow 1+r-1=1.06-1$
Simplify.
$\Rightarrow r=0.06$
$\Rightarrow r=6\%$.
Hence, the function represents exponential growth and the rate of growth is $6\%$.
