Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
3. Function Notation
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Exercise 29 Page 126

Each battery will die when the remaining charge is 0 %.

The tablet lasts longer. See solution.

Practice makes perfect

To determine which battery lasts longer, we can compare the number of hours it takes for each battery to have a 0 % charge. We will begin by finding when the laptop's battery dies from the given graph.

Notice on the graph that the laptop's battery charge reaches p=0 at t=5. This means that the laptop's battery lasts for 5 hours.


The Tablet

Next we will determine how long the tablet's battery lasts. It is given that the tablet's initial charge is 75 % and that the battery loses 12.5 % each hour. We can write each of these percents in decimal form as 0.75 and 0.125, respectively. Now we can use this information to write a linear equation in slope-intercept form. p=0.75-0.125t To graph this function, we will make a table of values.

t 0.75 - 0.125t p
0 0.75 - 0.125( 0) 0.75
2 0.75 - 0.125( 2) 0.5
4 0.75 - 0.125( 4) 0.25
6 0.75 - 0.125( 6) 0

Now we will plot the found ordered pairs in a coordinate plane. We can also draw a line connecting the points.

Notice on the graph that the tablets's battery charge reaches p=0 at t=6. This means that the tablet's battery lasts more than 6 hours. Therefore, the tablet lasts longer than the laptop. To check our answer, we can substitute 0 for p into the tablet's battery equation and solve for t.
p=0.75-0.125t
0=0.75-0.125t
0.125t=0.75
t=6
We can see that we obtained the same answer. Therefore, we can confirm that the tablet's battery life lasts longer than the laptop's battery life.