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The Natural Base e

The Natural Base e 1.9 - Solution

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We want to rewrite the exponential function in the form y=a(1+r)ty=a(1+r)^t or y=a(1r)t.y=a(1-r)^t. To do so, we will use the Power of a Power Property.
y=0.5e0.8ty=0.5e^{0.8t}
y=0.5(e0.8)ty=0.5\left( e^{0.8} \right) ^{t}
y=0.5(2.226)ty=0.5(2.226)^t
y=0.5(1+1.226)ty=0.5(1+1.226)^t
Note that the obtained formula involves addition. Therefore, it represents exponential growth. Finally, we will multiply r=1.226r=1.226 by 100100 to calculate the percent rate of change. 1.226×100=122.6% growth\begin{gathered} 1.226 \times 100 = 122.6\, \% \text{ growth} \end{gathered}