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We want to rewrite the exponential function in the form $y=a(1+r)^t$ or $y=a(1-r)^t.$ To do so, we will use the Power of a Power Property.
$y=0.5e^{0.8t}$
$y=0.5\left( e^{0.8} \right) ^{t}$
$y=0.5(2.226)^t$
$y=0.5(1+1.226)^t$
Note that the obtained formula involves addition. Therefore, it represents exponential growth. Finally, we will multiply $r=1.226$ by $100$ to calculate the percent rate of change. $\begin{gathered} 1.226 \times 100 = 122.6\, \% \text{ growth} \end{gathered}$