We are given a table that shows the percent y in decimal form of battery power remaining x hours after you turn on a laptop computer.
Hours, x
0
2
4
Power Remaining, y
1.0
0.6
0.2
We want to write a linear function that relates y to x. To do so, remember that functions written in slope-intercept form follow a specific format.
y= mx+ b
In this form, m is the slope and b is the y-intercept. We need to identify these values using the given table. Let's start by substituting the points (0,1) and (2,0.6), into the slope formula and calculating m.
We calculated that the slope s - 0.2. Now, remember that the y-intercept is the y-value where the line crosses the y-axis. It occurs when x=0. From the table we can see that when x=0, the value of y= 1.
Hours, x
0
2
4
Power Remaining, y
1.0
0.6
0.2
The function intercepts the y-axis at (0, 1). Therefore, the value of b is 1. Now that we have the slope and the y-intercept, we can write a function for the line that passes through the given points.
y= - 0.2x+ 1
Finally, let's draw the given points on a coordinate plane and draw a line that passes through them.
Recall the function obtained in Part A.
y= - 0.2x+ 1
Here, y represents the battery power and x the number of hours. The slope of the function represents the power lost each hour and the y-intercept represents the amount of power at the beginning. Therefore, the power at the beginning was 100 percent and it decreases 20 percent each hour.
We want to find the number of hours it will take to get 75 percent of battery power. Since the y-values represent the power remaining in decimal form, a 75 percent of battery corresponds to y=0.75. Let's substitute this into the obtained equation and solve it for x.
