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

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: - \( f(50) = 9 \)