When Nachelle left her house this morning, her cell phone was 32% charged and it then started to lose 4% charge for each hour thereafter. Write an equation for B, commaB, in terms of t, commat, representing the charge remaining in Nachelle's battery, as a percentage, tt hours after Nachelle left her house.

1 answer

To represent the charge remaining in Nachelle's battery as a percentage, we will denote the charge \( B \) as a function of time \( t \) (in hours).

Initially, when Nachelle left her house, her phone was charged to 32%. She loses 4% of the charge for each hour. Therefore, the equation for the charge remaining in her battery, \( B(t) \), can be written as:

\[ B(t) = 32 - 4t \]

where:

  • \( B(t) \) is the charge remaining in the battery as a percentage \( t \) hours after Nachelle left her house,
  • \( 32 \) is the initial battery percentage,
  • \( 4t \) represents the percentage lost after \( t \) hours.

Make sure that \( t \) does not exceed \( 8 \) hours, as the battery would go below 0% after that. Thus, \( B(t) \) should ideally be evaluated for \( t \) in the range of \( [0, 8] \).