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{{ printedBook.courseTrack.name }} {{ printedBook.name }} In order to match the function with its graph, we will first determine the type of the given function, then plot the graph. Lastly, we will compare the outcome with graphs given in the exercise.

To determine whether the given function represents exponential growth or exponential decay, let's recall two properties of the natural base exponential function, $y=ae_{rx}.$

$y=ae_{rx}$ | |
---|---|

$a>0$ and $r>0$ | $a>0$ and $r<0$ |

Exponential growth function | Exponential decay function |

Let's now consider the given function.
$y=4e_{-0.5x} $
Since $a=4$ is *greater than* zero and $r=-0.5$ is *less than* zero, the function is an **exponential decay** function.

Next, let's make a table of values to graph the function.

$x$ | $4e_{-0.5x}$ | $y=4e_{-0.5x}$ |
---|---|---|

$-1$ | $4e_{-0.5(-1)}$ | $≈6.59$ |

$0$ | $4e_{-0.5(0)}$ | $4$ |

$1$ | $4e_{-0.5(1)}$ | $≈2.43$ |

Finally, we will plot the points and connect them with a smooth curve.

Since $y=4e_{-0.5x}$ is an **exponential decay** function and the points $(-1,6.59)$ and $(0,4)$ belong to its graph, we can conclude that it is represented by the graph in choice **B**.