Final answer:
To determine how many hours after leaving his house it would take until the phone's battery level got down to 31.5%, we can use the linear relationship between time and battery charge remaining percentage.
Step-by-step explanation:
To determine how many hours it would take until the phone's battery level reaches 31.5%, we can use the linear relationship between t (hours) and B (battery charge remaining as a percentage).
- t = 1.5, B = 38.25
- t = 6, B = 18
- t = 8, B = 9
We can see that the battery charge is decreasing linearly over time. To find the equation of this linear relationship, we can use the two points: (1.5, 38.25) and (8, 9). Using the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, we can find the values of m and b.
Using the two points (1.5, 38.25) and (8, 9), we can calculate the slope m: m = (9 - 38.25) / (8 - 1.5) = -29.25 / 6.5 = -4.5
Then, we can substitute one of the points into the equation y = mx + b to find b. Let's use the point (1.5, 38.25): 38.25 = -4.5 * 1.5 + b. Solving for b, we get b = 45.75
Now that we have the equation of the line, y = -4.5x + 45.75, we can set y (battery charge as a percentage) to 31.5 and solve for x (hours): 31.5 = -4.5x + 45.75.
Subtracting 45.75 from both sides gives -14.25 = -4.5x. Dividing both sides by -4.5 gives x = 3.
Therefore, it would take 3 hours after leaving his house for the phone's battery level to reach 31.5%.