Question
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The owner of a small restaurant is out of rice, so they buy 75 kilograms of * 2 points rice. Each week, the restaurant uses 4.5 kilograms of rice. Functiont gives the remaining amount of rice, in kilograms, as a function of the number of weeks W, since the restaurant owner bought the rice.use Use function notation to write a rule that defines \( r \) (w) \( r(w)=75-4.5 \mathrm{~W} \) \( r(w)=75 \) \( r(4.5)=7.5 \)

Ask by Stuart Martin. in the United States
Mar 20,2025

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Tutor-Verified Answer

Answer

The remaining rice after \(w\) weeks is given by \( r(w) = 75 - 4.5w \).

Solution

The restaurant starts with \(75\) kilograms of rice. Each week, the restaurant uses \(4.5\) kilograms. Therefore, after \(w\) weeks, the amount of rice used is \(4.5w\) kilograms. To get the remaining rice, subtract the used amount from the initial amount: \[ r(w) = 75 - 4.5w \] Thus, the function \(r(w)\) that gives the remaining rice in kilograms after \(w\) weeks is: \[ r(w) = 75 - 4.5w \]

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The remaining amount of rice can be modeled by the equation \( r(w) = 75 - 4.5w \), where \( r(w) \) represents the amount of rice left in kilograms after \( w \) weeks. This function shows how the initial stock decreases as the restaurant uses a fixed amount each week, making it easy for the owner to predict when they'll need to restock. To avoid running out of rice unexpectedly, the restaurant owner should plan ahead! By using the function, they can determine how many weeks it will take to deplete the stock. For instance, to find when the rice will be exhausted, set \( r(w) = 0 \) and solve: \( 75 - 4.5w = 0 \). This will give them a clear timeline for placing their next order and maintaining smooth operations.

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