Answer
The function represents exponential decay and the rate of decay is $20\%$
Work Step by Step
The given function is
$\Rightarrow m(t)=(\frac{4}{5})^t$
$\Rightarrow m(t)=(0.8)^t$
$\Rightarrow m(t)=1(1-0.2)^t$
The function is of the form
$y=a(1-r)^t$, where $1-r<1$.
So, it represents exponential decay.
Decay factor is
$\Rightarrow 1-r=0.8$
Add $r-0.8$ to each side.
$\Rightarrow 1-r+r-0.8=0.8+r-0.8$
Simplify.
$\Rightarrow 0.2=r$.
$\Rightarrow r=20\%$.
Hence, the function represents exponential decay and the rate of decay is $20\%$.
