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A car is purchased for 15,000. Each year it loses 30% of it's value. After how many years will the car be worth 4600 or less. Write the smallest possible whole number answer

A car is purchased for 15000 Each year it loses 30 of its value After how many years will the car be worth 4600 or less Write the smallest possible whole number class=

Respuesta :

We will have the following:

[tex]\begin{gathered} 4600=15000(0.7)^x\Rightarrow\frac{23}{75}=(0.7)^x \\ \\ \Rightarrow ln(\frac{23}{75})=xln(0.7)\Rightarrow x=\frac{ln(23/75)}{ln(0.7)} \\ \\ \Rightarrow x=3.313924675...\Rightarrow x\approx3 \end{gathered}[/tex]

So, the after approximately 3 years the car will be worth $4600 or less.

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