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The dollar value v (t) of a certain car model that is t years old given by the following exponential function. v(t) =19,900(0.90) tFind the initial value if the car and the value after 12 years. Round your answers to the nearest dollar as necessary.

Respuesta :

Given

[tex]v(t)=19,900(0.90)^t[/tex]

Procedure

Initial value

[tex]\begin{gathered} v(0)=19,900(0.90)^0 \\ v(0)=19,900 \end{gathered}[/tex]

19,900 initial value of the car

value after 12 years

[tex]\begin{gathered} v(12)=19,900(0.90)^{12} \\ v(12)=19,900\cdot0.2824 \\ v(12)=5,620.34 \end{gathered}[/tex]

$5,620.34 value of the car after 12 years

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