Question

question
when khloe left her house in the morning, her cell phone battery was partially charged. the charge remaining in khloes battery, as a percentage, can be modeled by the equation ( b = 45 - 4.5t ), where ( t ) is the number of hours since khloe left her house. what is the ( x )-intercept of the equation and what is its interpretation in the context of the problem?
answer attempt 1 out of 2
the ( x )-intercept of the function is which represents

• the charge of the battery when khloe left her house
• the percentage charge that khloes phone loses each hour
• the number of hours until khloes phone dies
• the charge of the battery when khloe woke up

Explanation:

Step1: Recall the concept of x - intercept

In the equation of a line \(y = mx + b\) (in this case \(B=45 - 4.5t\), where \(B\) is similar to \(y\) and \(t\) is similar to \(x\)), the \(x\) - intercept is found by setting \(y = 0\) (or \(B = 0\) in our context). The \(x\) - intercept represents the value of \(x\) when \(y = 0\).

Step2: Analyze the physical meaning

When \(B = 0\) (battery charge is \(0\%\)), we solve the equation \(0=45 - 4.5t\) for \(t\). The variable \(t\) represents the number of hours since Khloe left her house. Solving \(4.5t=45\) gives \(t = 10\). This \(t\) value (the \(x\) - intercept) represents the number of hours until Khloe's phone dies.

Answer:

The number of hours until Khloe's phone dies