Question

The amount of garbage, G, produced by a city with population p is given by G=f(p). G is measured in tons per week, and p is measured in thousands of people. The town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function f. Explain the meaning of the statement f(5)=2.

Answer 1

• The given information in terms of the function f can be expressed as,

         $13=f(45)$

• The statement of $2=f(5)$ expression is a town has a population of 5000 and produces 5 tons of garbage each week.

How to convert statement to the function?

To convert the statement into the function,

• Read it carefully.
• Identify the factors of function.
• Express them in a balanced function form.

Given information-

The population of the Tola town is 40000.

The total amount of garbage each week Tola town produces is 13 tons.

The amount of garbage, G, produced by a city with population p is given by,

$G=f(p)$

Here, G is measured in tons per week, and p is measured in thousands of people.

• 1) In the given problem the garbage produced per week $G$ is 13 tons and number of people $p$ is 45 thousand. Thus replace the values in the given equation to find required equation as,

         $13=f(45)$

Thus the given information in terms of the function f can be expressed as,

$13=f(45)$

• 2) Function given is,

       

$f(5)=2$

Rewrite it as,

$2=f(5)$

Compare it with the general expression of problem.

Hence the statement of $2=f(5)$ expression is a town has a population of 5000 and produces 5 tons of garbage each week.

Hence,

• The given information in terms of the function f can be expressed as,

         $13=f(45)$

• The statement of $2=f(5)$ expression is a town has a population of 5000 and produces 5 tons of garbage each week.

Learn more about the function here;

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