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Matt purchases a used car for [tex]\$7000[/tex]. The value of the car decreases at a rate of [tex]12\%[/tex] per year.

Choose the exponential equation that represents this situation.

A. [tex]y = 7000(0.88)^x[/tex]

B. [tex]y = 7000(1.12)^x[/tex]

C. [tex]y = 7000 - 12x[/tex]

D. [tex]y = 7000(0.12)^x[/tex]

Answer :

The car's initial value is \[tex]$7000. Since the car depreciates by 12% per year, after one year it retains only 88% of its value. In other words, the multiplier every year is

$[/tex][tex]$1 - 0.12 = 0.88.$[/tex][tex]$

Thus, after $[/tex]x[tex]$ years the value of the car is given by the exponential equation

$[/tex][tex]$y = 7000 \cdot (0.88)^x.$[/tex]$

This corresponds to the equation in the first option.

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