Math Problem Statement
UNL has decided to gradually transition from one online gradebook system to another. The percentage of professors still using the old system years after Fall 2015 is given by B(t)=100-18t. Find domain
Solution
To find the domain of the function , we need to determine the range of values for which the function is defined, based on the context of the problem.
Analysis of the Function
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Understanding the Context:
- represents the percentage of professors still using the old system.
- represents the number of years after Fall 2015.
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Mathematical Constraints:
- The percentage of professors still using the old system, , must be between 0% and 100%. Therefore:
- Substituting the function into the inequality:
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Finding the Valid Range for :
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First, consider the lower bound :
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Now, consider the upper bound :
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Combining these two results gives:
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Conclusion
The domain of the function is: [ [0, \frac{100}{18}] \quad \text{or approximately} \quad [0, 5.56] ]
This means the function is valid for values of ranging from 0 to approximately 5.56 years after Fall 2015. After about 5.56 years, the percentage of professors still using the old system would reach 0%, so the function is not defined beyond that point.
Would you like more details on any part of this solution, or do you have any other questions?
Related Questions
- What is the value of exactly 3 years after Fall 2015?
- How long will it take until only 50% of professors are still using the old system?
- What is the rate of change of the percentage of professors using the old system per year?
- If the function were modified to , how would the domain change?
- How would you represent the situation graphically, and what does the slope represent?
Tip: Always check the context of a problem to determine reasonable domains and ranges for functions!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Functions
Domain and Range
Formulas
B(t) = 100 - 18t
Theorems
Linear Inequality
Suitable Grade Level
Grades 9-12
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