The Natural Base e

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}

a^{m\cdot n}=\left(a^{m}\right)^{n}

y=0.5\left( e^{0.8} \right) ^{t}

UseCalcUse a calculator

y=0.5(2.226)^t

WriteSumWrite as a sum

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}

The Natural Base e 1.9 - Solution