Long description: Block6_FigNEW1

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• The graph shows three distinct curves plotted on a set of axes where the horizontal axis represents time, labeled as \(t\), and the vertical axis represents the function value, labeled as \(y\).
• The axes are marked with numerical increments, ranging from \(-2\) to \(2\) on the time axis and from \(-2\) to \(16\) on the \(y\)-axis.
• Three exponential functions are drawn: \(e^t\), \(2e^t\), and \(e^{2t}\).
• All three curves are monotonically increasing, starting near the origin and rising steeply as \(t\) increases.
• At \(t=0\), the graph shows the following values: the curve \(e^t\) passes through the point \((0, 1)\); the curve \(2e^t\) passes through the point \((0, 2)\); and the curve \(e^{2t}\) passes through the point \((0, 1)\).
• As \(t\) increases to \(2\), the values are approximately: \(e^t \rightarrow e^2 \text{ (about } 7.4)\text{, } 2e^t \rightarrow 2e^2 \text{ (about } 14.8)\text{, and } e^{2t} \rightarrow e^4 \text{ (about } 54.6)\text{.}
• The curves illustrate that for positive values of \)t\(, the function \)e^{2t}\( grows much faster than \)2e^t\(, which in turn grows faster than \)e^t$.