Question

which graph shows the number of minutes, y, that the battery will power a video camera after it has been recharged x times?

Explanation:

Step1: Analyze the relationship

As the number of recharges \(x\) increases, the battery life \(y\) (in minutes) should decrease. Also, the decrease is not linear. Each recharge reduces the battery's capacity, but the rate of decrease slows down over time.

Step2: Evaluate each graph

• Graph \(W\): The decrease is very slow and almost linear - not an exponential decay.
• Graph \(X\): Linear decrease. But battery - recharge relationship is not linear (battery degradation is more complex, not a constant rate of decrease).
• Graph \(Z\): The \(x\) - axis range is too small (\(x\) only goes up to 40 while the other graphs have \(x\) up to 80).
• Graph \(Y\): Shows a non - linear (exponential - like) decrease. As \(x\) (number of recharges) increases, \(y\) (battery life) decreases in a non - linear fashion.

Answer:

The graph \(Y\) shows the correct relationship.