Answer
Initial amount $a=10$
Rate of growth $r=40\%$
At $t=5, y=53.8$
Work Step by Step
The given expression is
$\Rightarrow y=10(1+0.4)^t$
The standard form of the exponential growth function is
$y=a(1+r)^t$
Initial amount $a=10$
Rate of growth $r=0.4=40\%$
Substitute $5$ for $t$.
$\Rightarrow y=10(1+0.4)^5$
Simplify.
$\Rightarrow y=10(1.4)^5$
Evaluate the power.
$\Rightarrow y=10(5.37824)$
Simplify.
$\Rightarrow y=53.7824$
Round to the nearest tenth.
$\Rightarrow y=53.8$.
