Question

question
when nathaniel left his house in the morning, his cell phone battery was partially charged. the charge
remaining in nathaniels battery, as a percentage, can be modeled by the equation ( b = 52 - 6.5t ), where ( t )
is the number of hours since nathaniel left his house. what is the slope of the equation and what is its
interpretation in the context of the problem?
answer attempt 1 out of 2
the slope of the function is which reveals
the percentage charge that nathaniels phone loses each hour.
the rate that nathaniels phone gains charge per hour
the charge of the battery when nathaniel left his house.
the number of hours until nathaniels phone dies

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(B = 52-6.5t\), we can rewrite it as \(B=-6.5t + 52\).

Step2: Identify the slope

Comparing \(B=-6.5t + 52\) with \(y = mx + b\), we can see that \(m=-6.5\). The slope \(m\) represents the rate of change of the dependent variable with respect to the independent variable. In the context of the problem, \(B\) (battery charge as a percentage) is the dependent variable and \(t\) (number of hours since Nathaniel left his house) is the independent variable.

Answer:

The slope of the function is \(-6.5\), which reveals the percentage charge that Nathaniel's phone loses each hour.