Answer
Initial amount $a=175$
Rate of growth $r=2.8\%$
$h(5)=200.9$
Work Step by Step
The given expression is
$\Rightarrow h(t)=175(1.028)^t$
$\Rightarrow h(t)=175(1+0.028)^t$
The standard form of an exponential growth function is
$y=a(1+r)^t$
Initial amount $a=175$
Rate of growth $r=0.028=2.8\%$
Substitute $5$ for $t$.
$\Rightarrow h(5)=175(1.028)^5$
Evaluate the power.
$\Rightarrow h(5)=175(1.14806261049)$
Simplify.
$\Rightarrow h(5)=200.910956836$
Round to the nearest tenth.
$\Rightarrow h(5)=200.9$
