Question

when elizabeth left her house in the morning, her cell phone battery was partially charged. the charge remaining in elizabeths battery, as a percentage, can be modeled by the equation ( b = -5t + 40 ), where ( t ) is the number of hours since elizabeth left her house. what is the ( x )-intercept of the equation and what is its interpretation in the context of the problem?
the ( x )-intercept of the function is which represents
answer attempt 1 out of 2
the number of hours until elizabeths phone dies
the charge of the battery when elizabeth left her house
the percentage charge that elizabeths phone loses each hour
the charge of the battery when elizabeth woke up

Explanation:

Step1: Recall the concept of x - intercept

The x - intercept of a function \(y = f(x)\) is found by setting \(y = 0\). In the linear function \(B=-5t + 40\), we set \(B = 0\) (since \(B\) represents the battery charge and when the phone dies, \(B = 0\)).

Step2: Solve for \(t\)

Set \(B = 0\) in the equation \(0=-5t + 40\).
Add \(5t\) to both sides: \(5t=40\).
Divide both sides by \(5\): \(t=\frac{40}{5}=8\).

Answer:

The number of hours until Elizabeth's phone dies.