Answer
The function represents exponential decay and the rate of decay is $16\%$.
Work Step by Step
The given function is
$\Rightarrow f(t)=6(0.84)^{t-4}$
Use $(a)^{m-n}=\frac{a^m}{a^n}$.
$\Rightarrow f(t)=6\frac{(0.84)^{t}}{(0.84)^{4}}$
$\Rightarrow f(t)=\frac{6}{(0.84)^{4}}(0.84)^{t}$
$\Rightarrow f(t)=\frac{6}{(0.84)^{4}}(1-0.16)^{t}$
The function is of the form
$y=a(1-r)^t$, where $1-r<1$.
So, it represents exponential decay.
Decay factor is
$\Rightarrow 1-r=0.84$
Add $r-0.84$ to each side.
$\Rightarrow 1-r+r-0.84=0.84+r-0.84$
Simplify.
$\Rightarrow 0.16=r$.
$\Rightarrow 16\%=r$.
Hence, the function represents exponential decay and the rate of decay is $16\%$.
