Question

An automobile purchased for $35,000 is worth $2100 after 7 years. Assuming that the car’s value depreciated steadily from year to year, what was it worth at the end of the third year

Answer 1

At the end of the third year, the worth is 10,479.64 dollars

Explanation:

This problem can be modeled by an exponential function since we have that  the car’s value depreciated steadily from year to year, that is, we have a constant ratio. So:

$c(x)=ab^x \\ \\ a:Initial \ value \\ \\ b:constant \ ratio \\ \\ x:Number \ of \ years$

The automobile was purchased for $35,000, so this is the initial value:

$a=35,000$

After 7 years it is worth $2,100:

$Substituting \ values: \\ \\ 2,100=35,000b^7 \\ \\ b^7=0.06 \\ \\ b=\sqrt[7]{0.06} \\ \\ b=0.669$

So our exponential function becomes:

$c(x)=ab^x \\ \\ c(x)=35,000(0.669)^x$

At the end of the third year, the worth is:

$c(3)=35,000(0.669)^3 \\ \\ c(3)=\ 10,479.64$

At the end of the third year, the worth is 10,479.64 dollars

Learn more:

Simple interest: brainly.com/question/12354888

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