Questions: Sean purchased a piece of sports memorabilia for 5900, and it is expected to increase in value by 9% per year. Write a function y to represent the value of the piece of sports memorabilia after x years. y=5900(1.09)

Solution Steps

To solve this problem, we need to create a function that models the exponential growth of the value of the sports memorabilia. The initial value is $5900, and it increases by 9% each year. This can be represented by the formula \( y = 5900 \times (1.09)^x \), where \( y \) is the value after \( x \) years.

The value of the sports memorabilia increases by \(9\%\) each year. This can be modeled using an exponential growth function. The general formula for exponential growth is:

\[ y = a \times (1 + r)^x \]

where:

• \(y\) is the future value,
• \(a\) is the initial value,
• \(r\) is the growth rate,
• \(x\) is the number of years.

In this problem, the initial value \(a\) is \(5900\), and the growth rate \(r\) is \(0.09\) (since \(9\%\) is equivalent to \(0.09\)). Substituting these values into the formula gives:

\[ y = 5900 \times (1.09)^x \]

Final Answer