• The car loses value at a rate of 7.5% per year. This means it retains 92.5% of its value each year.
• The retention rate is \(1 - 0.075 = 0.925\).
• The value of the car after \(x\) years can be represented by \(y = 35000( 0.925) ^ x\).

Supplemental Knowledge

• Exponential decay describes a process where a quantity decreases at a rate proportional to its current value. This is often used to model depreciation, radioactive decay, and cooling processes. The general form of the exponential decay equation is:
  \[y = y_ 0 \cdot ( 1 - r) ^ x\]
  where:
• \(y\) is the final amount.
• \(y_ 0\) is the initial amount.
• \(r\) is the rate of decay (expressed as a decimal).
• \(x\) is the number of time periods.
  In this case, the car's value decreases by 7.5% each year, so \(r = 0.075\).

Life in Context

Imagine you bought a new gadget for 1,000 that loses 10% of its value each year. After one year, it would be worth $900; after two years, it would be worth $810, and so on. Understanding exponential decay helps you predict how long your investments or purchases will retain their value.

Grasping concepts like exponential decay can be crucial for financial planning and asset management. If you're looking to deepen your understanding of algebraic principles or need assistance with specific math problems, UpStudy offers a variety of calculators and educational resources tailored for algebra.
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