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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We can model the value of the car by using the exponential decay function. $V(t)=a(1−r)_{t} $ The function can be used to find the value of the car $V(t)$ after $t$ time period, where $a$ is the initial value of the car and $r$ is the percent of decrease per time period. For our model, $a=20000$ and $r=0.15.$ $V(t)=20000(1−0.15)_{t}⇔V(t)=20000(0.85)_{t} $ Now that we have the function, we can graph the function showing the value of the car for the first twenty years. To do so, we will first make a table of values.

$t$ | $20000(0.85)_{t}$ | $V(t)=20000(0.85)_{t}$ |
---|---|---|

$5$ | $20000(0.85)_{5}$ | $≈8874$ |

$10$ | $20000(0.85)_{10}$ | $≈3937$ |

$15$ | $20000(0.85)_{15}$ | $≈1747$ |

$20$ | $20000(0.85)_{20}$ | $≈775$ |

Let's now plot and connect the points $(5,8874),$ $(10,3937),$ $(15,1747),$ and $(20,775)$ with a smooth curve.