Answer
Initial amount $a=475$
Rate of decay $r=50\%$
At $t=3, f(3)=59.4$.
Work Step by Step
The given expression is
$\Rightarrow f(t)=475(0.5)^t$
$\Rightarrow f(t)=475(1-0.5)^t$
The standard form of an exponential decay function is
$y=a(1-r)^t$
Initial amount $a=475$
Rate of decay $r=0.5=50\%$
Substitute $3$ for $t$.
$\Rightarrow f(3)=475(0.5)^3$
Evaluate the power.
$\Rightarrow f(3)=475(0.125)$
Simplify.
$\Rightarrow f(3)=59.375$
Round to the nearest tenth.
$\Rightarrow f(3)=59.4$.
