Question

When Camden left his house in the morning, his cell phone battery was partially charged. Camden's phone lost battery life at a rate of 4% each hour and 2 hours after leaving his house, the battery had 24% remaining battery life. Write an equation for the function

B
(
t
)
,
B(t), representing the charge remaining in Camden's battery, as a percentage,
t
t hours after Camden left his house.

Answer 1

B(t) = (32 - 4t)% when 0 ≤ t ≤ 8

= 0 % for t > 8

Explanation:

According to the question, when Camden left his house in the morning,

the charge in his battery was,

`(24 + 2 * 4)` %

= 32 %

So, the charge in Camden's phone, t hours after he left the house is given by,

B(t) = (32 - 4t) % ------------(1)

Now clearly in (1),

0 ≤ t ≤
`\frac {32}{4}`

⇒ 0 ≤ t ≤ 8 since charge in mobile phone can't have a negative percentage and time after Camden left home can't be negative.

So,

B(t) = (32 - 4t)% when 0 ≤ t ≤ 8

= 0 % for t > 8