Question 18 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 50,000 and produces 9 tons of garbage each week. Express this information in terms of the function $$ f $$ $$ f(50)=9 $$ $$ f=9 / 50 $$ $$ f(9)=50 $$ Question Help: Submit Question

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UpStudy AI · Accepted Answer

To express the information given in the problem in terms of the function $$ f $$, we need to analyze the relationship between the population $$ p $$ and the amount of garbage $$ G $$.

1. **Extract Known Conditions:**
   - The population of Tola is $$ p = 50,000 $$ people, which is equivalent to $$ p = 50 $$ in thousands.
   - The amount of garbage produced is $$ G = 9 $$ tons per week.

2. **Expressing the Information:**
   - The function $$ f(p) $$ represents the amount of garbage produced per week based on the population in thousands.
   - Given that $$ f(p) $$ gives the amount of garbage produced for a population $$ p $$, we can substitute the known values into the function.

3. **Substituting Values:**
   - We know that when $$ p = 50 $$, $$ G = 9 $$. Therefore, we can express this as:
     $$
     f(50) = 9
     $$

4. **Finding the Function Value:**
   - To find the value of $$ f $$ in terms of $$ p $$, we can rearrange the equation:
     $$
     f(50) = 9 \implies f = \frac{9}{50}
     $$

5. **Evaluating Other Options:**
   - The option $$ f(9) = 50 $$ does not hold true since it does not correspond to the given data.

Thus, the correct expression based on the information provided is:
$$
f(50) = 9
$$
and
$$
f = \frac{9}{50}
$$

The correct answer is:
- $$ f(50) = 9 $$
$$ f(50) = 9 $$

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