Math Problem Statement
Solution
The given problem involves a function , where represents the amount of garbage (measured in tons per week) produced by a city with a population (measured in thousands of people).
Problem Breakdown:
- Population (p): The town of Tola has a population of 25,000 people. In terms of thousands, this means .
- Garbage (G): The town produces 10 tons of garbage each week. So, .
This information needs to be expressed in terms of the function , which relates the population to the garbage produced .
Solution:
Since and , we can write this in the form: This means that for a population of 25,000 people, the town produces 10 tons of garbage per week.
Thus, the correct answer is:
Answer:
The first option, , is correct.
Would you like more details or have any other questions?
Here are some related questions to deepen your understanding:
- How would the function look like if the relationship between population and garbage production were linear?
- What is the interpretation of in the context of this problem?
- How would you express the function if the population were 50,000 and the garbage produced was 20 tons?
- How would changes in population affect garbage production if the relationship was proportional?
- How would you compute if given a nonlinear relationship between garbage production and population?
Tip: Always pay attention to the units when setting up functions from real-world problems!
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Math Problem Analysis
Mathematical Concepts
Functions
Algebra
Modeling with Functions
Formulas
G = f(p)
Theorems
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Suitable Grade Level
Grades 9-11