IDNLearn.com provides a collaborative environment for finding accurate answers. Get step-by-step guidance for all your technical questions from our dedicated community members.
Sagot :
To find the value [tex]\( y \)[/tex] of Ty's computer after [tex]\( x \)[/tex] years, where the computer depreciates at a rate of [tex]\( 12\% \)[/tex] per year, we need to use the depreciation formula. Depreciation at a constant percentage rate indicates exponential decay.
The value of the computer after [tex]\( x \)[/tex] years can be represented by the equation:
[tex]\[ y = P \times (1 - r)^x \][/tex]
where:
- [tex]\( y \)[/tex] is the value of the computer after [tex]\( x \)[/tex] years,
- [tex]\( P \)[/tex] is the initial value of the computer,
- [tex]\( r \)[/tex] is the depreciation rate,
- [tex]\( x \)[/tex] is the number of years.
Given:
- [tex]\( P = 499 \)[/tex] (the initial value of the computer in dollars),
- [tex]\( r = 0.12 \)[/tex] (the depreciation rate as a decimal).
Therefore, the value [tex]\( y \)[/tex] of Ty's computer after [tex]\( x \)[/tex] years is:
[tex]\[ y = 499 \times (1 - 0.12)^x \][/tex]
Simplifying the equation, we have:
[tex]\[ y = 499 \times 0.88^x \][/tex]
Thus, the equation for the value of his computer [tex]\( x \)[/tex] years after he bought it is:
[tex]\[ y = 499 \times 0.88^x \][/tex]
This equation shows how the computer's value decreases exponentially over time with an annual depreciation rate of [tex]\( 12\% \)[/tex].
The value of the computer after [tex]\( x \)[/tex] years can be represented by the equation:
[tex]\[ y = P \times (1 - r)^x \][/tex]
where:
- [tex]\( y \)[/tex] is the value of the computer after [tex]\( x \)[/tex] years,
- [tex]\( P \)[/tex] is the initial value of the computer,
- [tex]\( r \)[/tex] is the depreciation rate,
- [tex]\( x \)[/tex] is the number of years.
Given:
- [tex]\( P = 499 \)[/tex] (the initial value of the computer in dollars),
- [tex]\( r = 0.12 \)[/tex] (the depreciation rate as a decimal).
Therefore, the value [tex]\( y \)[/tex] of Ty's computer after [tex]\( x \)[/tex] years is:
[tex]\[ y = 499 \times (1 - 0.12)^x \][/tex]
Simplifying the equation, we have:
[tex]\[ y = 499 \times 0.88^x \][/tex]
Thus, the equation for the value of his computer [tex]\( x \)[/tex] years after he bought it is:
[tex]\[ y = 499 \times 0.88^x \][/tex]
This equation shows how the computer's value decreases exponentially over time with an annual depreciation rate of [tex]\( 12\% \)[/tex].
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.