Question

the graph shows the percent ( p ) (in decimal form) of battery power remaining in a laptop computer after ( t ) hours of use. a computer initially has 75% of its battery power remaining and loses 12.5% per hour. which computers battery will last l explain. the tablet computer; the graph of the tablet computer has a slope of ( -0.125 ), which is less steep than ( -0.20 ), th slope of the graph of the laptop computer. the tablet computer; the graph of the tablet computer shows that when ( p(t)=0, t ) is 6, which is greater than 5. the laptop computer; the graph of the laptop computer has a slope of ( -0.20 ), which is steeper than ( -0.125 ), the

Explanation:

Step1: Analyze the graph

The graph shows the relationship between battery power remaining \(p\) (in decimal form) and hours of use \(t\). When \(p = 0\) (battery is dead), from the graph, for the tablet - like graph (assuming the given graph is for the tablet - like situation in the options), \(t = 6\).

Step2: Calculate for the laptop

The laptop has an initial power \(p(0)=0.75\) (75% in decimal) and a rate of change \(m=- 0.125\) (loses 12.5% per hour). Using the linear equation \(p(t)=mt + b\) (\(b = 0.75\), \(m=-0.125\)), when \(p(t)=0\), we solve \(0=-0.125t + 0.75\).

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Wait, no. Wait, the laptop's equation: If the laptop has \(p(0) = 0.75\) (75% in decimal) and slope \(m=-0.125\) (since it loses 12.5% per hour). Using \(p(t)=mt + p(0)\), when \(p(t) = 0\), \(0=-0.125t+0.75\), \(t = 6\). But looking at the options, maybe there was a mis - understanding.

Assume the graph is for a device (say device A) and the laptop is device B.
For the graph (device A): When \(p = 0\), \(t = 6\) (from the \(x\) - intercept of the line \(p\) vs \(t\)).
For the laptop (device B): Using the formula \(p(t)=-0.125t + 0.75\). Set \(p(t)=0\), \(t=\frac{0.75}{0.125}=6\) (but wait, no, if the laptop loses 12.5% per hour. Wait, no, the slope of the line in the graph: The line passes through \((0,1)\) and \((5,0)\). The slope \(m=\frac{0 - 1}{5-0}=-0.2\).
The laptop has \(p(0) = 0.75\) and \(m=-0.125\). Using \(p(t)=-0.125t + 0.75\), when \(p(t)=0\), \(t=\frac{0.75}{0.125}=6\).
The graph (assuming it's for a different device, say the first device in the options). The \(x\) - intercept (when \(p = 0\)) of the graph is \(t = 5\) (from the line passing through \((0,1)\) and \((5,0)\)).

Answer:

the tablet computer; The graph of the tablet computer shows that when \(p(t)=0\), \(t\) is \(6\), which is greater than \(5\).