Answer
Initial amount $a=0.5$
Rate of decay $r=25\%$
At $t=3,y\approx 0.2$
Work Step by Step
The given expression is
$\Rightarrow y=0.5(\frac{3}{4})^t$
$\Rightarrow y=0.5(1-\frac{1}{4})^t$
The standard form of an exponential decay function is $y=a(1-r)^t$
Initial amount $a=0.5$
Rate of decay $r=\frac{1}{4}=25\%$
Substitute $3$ for $t$.
$\Rightarrow y=0.5(\frac{3}{4})^3$
Evaluate the power.
$\Rightarrow y=0.5(0.421875)$
Simplify.
$\Rightarrow y=0.2109375$
Round to the nearest tenth.
$\Rightarrow y\approx 0.2$.
