Real-World Situation for Graph 2

Question

Scenario: A television purchased for $2,500 depreciates in value over time.

x: Number of years since the television was purchased
y: Remaining value in thousands of dollars
a: Initial value ($2,500)
b: Depreciation factor (0.9, meaning it retains 90% of the previous value each year)

write an equation for this

Answer 1

To model the depreciation of the television, we can use an exponential decay formula. The value of the television after \( x \) years can be calculated using the following formula:

\[ y = a \cdot b^x \]

Where:

• \( y \) is the remaining value of the television in thousands of dollars,
• \( a \) is the initial value in thousands of dollars (since the initial value is $2,500, we express it in thousands, which is \( 2.5 \)),
• \( b \) is the depreciation factor (in this case, \( 0.9 \)),
• \( x \) is the number of years since the television was purchased.

Substituting the values we have:

\[ y = 2.5 \cdot 0.9^x \]

This is the equation that represents the remaining value of the television over time as it depreciates.