Long description: Block7_Fig6_2

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A graph comparing two exponential functions, \(P = 12 e^{0.01t}\) and \(P = 12e^{0.02t}\), plotted against time.

Alt text: A graph comparing two exponential functions, \(P = 12 e^{0.01t}\) and \(P = 12e^{0.02t}\), plotted against time.

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  • The horizontal axis represents time, labeled \(t\), and ranges from zero to at least two hundred units.
  • The vertical axis represents a quantity labeled \(P\), with markings at two hundred fifty and five hundred units.
  • Two curves are plotted on the graph: one solid line and one dashed line.
  • The solid curve represents the function \(P = 12 e^{0.01t}\), which shows a slow, gradual increase from the origin.
  • The dashed curve represents the function \(P = 12e^{0.02t}\), which shows a much steeper, faster rate of increase compared to the solid curve.
  • At time \(t=0\), both curves start at the same vertical position on the \(P\)-axis.
  • As time \(t\) increases, the vertical distance between the dashed curve and the solid curve increases significantly, illustrating the difference in the growth rates of the two exponential functions.

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