The car loses value at a rate of 7.5% per year. This means the car retains \(100\% - 7.5\% = 92.5\% \) of its value each year. 
The equation representing the value of the car over time, where \(y\) is the value of the car and \(x\) is the number of years, is:
\[y = 35000 \times ( 0.925) ^ x\]

Supplemental Knowledge

Mathematically speaking, exponential decay refers to reducing an amount by an unchanging percentage rate over a specific amount of time - this process can be used as an analogy for depreciation, radioactive decay and population decrease.

1. Exponential Decay Formula:
   • The general formula for exponential decay is \(y = a( 1 - r) ^ x\), where:
     • \(y\) is the final amount.
     • \(a\) is the initial amount.
     • \(r\) is the decay rate (as a decimal).
     • \(x\) is the number of time periods.
2. Decay Rate:
   • If an item loses value at a rate of 7.5% per year, then the decay rate \(r\) would be 0.075.
   • The remaining value after each year would be \(1 - r = 1 - 0.075 = 0.925\).

Knowledge in Action

Consider investing in electronics like smartphones or laptops - they depreciate over time due to technological developments and wear and tear - just like John's car does each year.
Understanding exponential decay allows you to make educated investments and purchases based on current depreciation rates, by helping predict future values based on depreciation trends.

Understanding how values change over time can significantly impact your financial planning and investment strategies! At UpStudy, we provide comprehensive tools and resources to help you master algebraic concepts effortlessly.
For accurate calculations involving exponential decay, try UpStudy’s Algebra Functions Calculator today!