Question

1. a new truck that sells for $29,000 depreciates (decreases in value) 12% each year. which function models the value of the truck?

options:
$y = (0.88)(29,000)^x$
$y = 25,520(0.88)^x$
$y = 29,000(0.88)^x$
$y = (29,000)^x$

Explanation:

Step1: Recall Depreciation Formula

The formula for exponential depreciation is \( y = a(1 - r)^x \), where \( a \) is the initial value, \( r \) is the annual depreciation rate (as a decimal), and \( x \) is time in years.

Step2: Identify Values

Here, \( a = 29000 \) (initial price of the truck), \( r = 0.12 \) (12% depreciation, so \( 1 - r = 1 - 0.12 = 0.88 \)).

Step3: Form the Function

Substitute \( a = 29000 \) and \( 1 - r = 0.88 \) into the formula: \( y = 29000(0.88)^x \). We check the options: if an option is \( y = 29000(0.88)^x \) (correcting any misformatting like \( y=(0.88)(29000)^x \) which is wrong as it would be growth of 29000, not decay), this matches the depreciation model.

Answer:

\( y = 29000(0.88)^x \) (assuming the first option is \( y=(0.88)(29000)^x \) which is incorrect, and the correct form for exponential depreciation is \( y = a(1 - r)^x \) where \( a = 29000 \), \( r = 0.12 \), so \( 1 - r = 0.88 \), so the correct function should be \( y = 29000(0.88)^x \); if the options are as per the image, likely the first option's format is miswritten and the correct one is with 29000 as the initial value and 0.88 as the decay factor, so the correct option would be the one with \( y = 29000(0.88)^x \) (assuming the second option from left is \( y = 29000(0.88)^x \) if the first is misformatted))