Answer
Initial amount $a=25$
Rate of growth $r=20\%$
At $t=5,y=62.2$
Work Step by Step
The given expression is
$\Rightarrow y=25(1.2)^t$
$\Rightarrow y=25(1+0.2)^t$
The standard form of the exponential growth function is
$y=a(1+r)^t$
Initial amount $a=25$
Rate of growth $r=0.2=20\%$
Substitute $5$ for $t$.
$\Rightarrow y=25(1+0.2)^5$
Simplify.
$\Rightarrow y=25(1.2)^5$
Evaluate the power.
$\Rightarrow y=25(2.48832)$
Simplify.
$\Rightarrow y=62.208$
Round to the nearest tenth.
$\Rightarrow y=62.2$.
