Question

When Henry left his house in the morning, his cell phone battery was partially

charged. Let B represent the charge remaining in Henry's battery, as a percentage, t

hours since Henry left his house. A graph of B is shown below. Write an equation for

B then state the slope of the graph and determine its interpretation in the context of

the problem.

Answer 1

Explanation:

From the given graph, we can see that the initial charge on Henry's cell phone battery is at 80%, which is the value of B when t = 0.

The graph is a straight line, which means that the equation for B is a linear equation of the form B = mt + b, where m is the slope of the line and b is the y-intercept (the value of B when t = 0).

From the graph, we can see that when t = 12, B = 20. Therefore, we have the points (0, 80) and (12, 20) on the line.

Using these two points, we can find the slope of the line:

m = (change in B) / (change in t) = (20 - 80) / (12 - 0) = -5

Therefore, the equation for B is:

B = -5t + 80

The slope of the graph is -5, which represents the rate of change of the charge in Henry's cell phone battery. Specifically, the slope tells us that the battery charge is decreasing at a rate of 5% per hour.