in the morning, kinsley makes a pot of coffee. the pot fills quickly at a constant rate until just before…
in the morning, kinsley makes a pot of coffee. the pot fills quickly at a constant rate until just before the machine is finished, when the flow slows and then stops. after a moment, kinsley pours a mug of coffee for herself. she leaves the rest in the pot for her family to drink later. which graph could show the amount of coffee in the pot over time?
Answer
Explanation:
Step1: Analyze the coffee - making process
- First, the pot fills quickly at a constant rate. So, the graph should have a steep (constant slope) increasing line at the start as the amount of coffee in the pot increases with time.
- Then, just before the machine is finished, the flow slows and then stops. This means the rate of increase of coffee in the pot decreases (the slope of the line becomes less steep) until the amount of coffee stops increasing (the line becomes horizontal for a moment as the machine stops).
- After that, Kinsley pours a mug of coffee for herself. So, the amount of coffee in the pot should decrease (a line with a negative slope) as coffee is removed.
- Finally, she leaves the rest in the pot for her family. So, after pouring, the amount of coffee in the pot should remain constant (a horizontal line) because no more coffee is being added or removed (until the family drinks it, but the problem says she leaves it, so we assume a constant amount after pouring her mug).
Step2: Compare with the two graphs
- For the first graph: After pouring the mug, the amount of coffee becomes constant (the horizontal line at the end), which matches our analysis.
- For the second graph: After pouring the mug, the amount of coffee starts to increase again, which does not match the situation where she leaves the rest in the pot (there is no reason for the coffee amount to increase after she pours her mug and leaves the rest).