Question
- The dollar value of a moped is a function of the number of years,
, since the moped
was purchased. The function,
, is defined by the equation
.
What is the best choice of domain for the function
?
A.
B.
C.
D.
was purchased. The function,
What is the best choice of domain for the function
A.
B.
C.
D.
Ask by Warren Craig. in the United States
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The best choice for the domain is
.
Solution
The function
models the dollar value of a moped
years after its purchase. Here,
represents the number of years since the moped was bought.
Key Considerations for the Domain:
-
Non-Negative Time: Since
represents the time elapsed since the purchase, it cannot be negative. Negative values of would imply a time before the purchase, which isn’t relevant in this context. -
Practical Time Frame: While the function mathematically allows
to extend indefinitely, in practical scenarios, the value of a moped would typically be considered within a reasonable time frame (e.g., up to 10 years). Extending the domain to 100 years isn’t practical for assessing the value of a moped.
Given these considerations:
- Option A includes negative values, which are not applicable.
- Option B only covers negative values.
- Option C includes non-negative values up to 10 years, aligning well with practical considerations.
- Option D extends to 100 years, which is less practical.
Therefore, the best choice for the domain is:
C.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Beyond the Answer
When considering the function
, we realize that this equation models the depreciation of a moped over time. Given that
represents the number of years since the moped was purchased, it makes sense for
to start at 0 (the year of purchase) and extend into the future, capturing realistic scenarios of moped ownership.
Based on this understanding, the best choice for the domain of the function
is
or even
if we want to represent long-term value depreciation. However, usually, the context around vehicle depreciation leans more towards the first few years, making
a reasonable answer.
In practical terms, you’ve got a vehicle that’s losing value every year! Hop on your moped and take a ride, because that depreciation isn’t slowing down anytime soon! Remember that the longer you keep it, the less it’s worth, so consider your options responsibly!