Math Problem Statement

The amount of garbage, G, in tons per week, produced by a city with population p, measured in thousands of people, is given by G = f(p). The town of Nola has a population of 45,000 and produces 10 tons of garbage each week. Express this information in terms of the function f

Solution

Given the problem, the function G=f(p)G = f(p) represents the amount of garbage produced by a city based on its population. Here, GG is the amount of garbage in tons per week, and pp is the population in thousands of people.

Problem Details:

  • The population of the town of Nola, pp, is 45,000 people. Since pp is measured in thousands, we have: p=45,0001,000=45p = \frac{45,000}{1,000} = 45
  • The town produces 10 tons of garbage each week, so G=10G = 10 tons.

Expressing the Information in Terms of the Function ff:

Using the given information, we can express the relationship as: f(45)=10f(45) = 10

This means that when the population pp is 45 (i.e., 45,000 people), the function ff produces a value of 10 tons of garbage per week.

Would you like further details on how to interpret this function or explore related concepts?

Related Questions:

  1. What would f(p)f(p) represent if the population were 60,000 people?
  2. How would you interpret f(50)=12f(50) = 12 in the context of this problem?
  3. If another town produces 15 tons of garbage each week with a population of 60,000, how would you express this using f(p)f(p)?
  4. How can you find the population that produces 20 tons of garbage per week if you know the function f(p)f(p)?
  5. If the population doubles, how might that affect the amount of garbage produced?

Tip: Expressing information in terms of a function allows you to see the relationship between variables, making it easier to predict outcomes for different inputs.

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Math Problem Analysis

Mathematical Concepts

Functions
Linear Equations

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9