When Lily left her house in the morning, her cell phone battery was partially charged. The charge remaining in Lily's battery, as a percentage, can be modeled by the equation B, equals, minus, 4, t, plus, 52, commaB=−4t+52, where tt is the number of hours since Lily left her house. What is the xx-intercept of the equation and what is its interpretation in the context of the problem?
Answer
To find the x-intercept of the equation, we need to determine when the battery charge drops to 0, which means B = 0.
0 = -4t + 52
Rearranging the equation, we get:
4t = 52
Dividing both sides by 4, we find:
t = 13
Therefore, the x-intercept of the equation is (13, 0).
In the context of the problem, the x-intercept represents the number of hours it takes for Lily's cell phone battery to completely run out of charge. So, in this case, it would take 13 hours for the battery to drain completely from the time Lily left her house.
whats the functions
The function in the given problem is B = -4t + 52.
what does this represent
The function B = -4t + 52 represents the remaining charge in Lily's cell phone battery, expressed as a percentage, in relation to the number of hours (t) since she left her house. The equation shows that the battery charge (B) decreases by 4% per hour since leaving the house, starting with a initial charge of 52%.
To find the x-intercept of an equation, we set the y-value (in this case B, representing the charge remaining in Lily's battery) to zero and solve for x.
Setting B = 0 in the equation -4t + 52 = 0, we can solve for t:
-4t + 52 = 0
-4t = -52
t = -52 / -4
t = 13
So the x-intercept of the equation is at t = 13.
Interpretation in the context of the problem:
The x-intercept represents the number of hours since Lily left her house when the charge remaining in her battery reaches zero. In this case, the x-intercept at t = 13 means that Lily's cell phone battery will be completely drained after 13 hours since she left her house.