Question

bailey starts playing a game on her cell phone with the battery fully charged and plays until the phone battery dies. while playing the game, the charge in baileys battery decreases by half a percent per minute.
a. write a function for the percent change in the battery while bailey is playing the game.
b. what are the domain and range of the function?
c. how long can bailey play the game?
a. write the function ( p(t) ) for the percent charge ( p ) after ( t ) minutes.
( p(t) = square )
(simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Identify the initial value and rate of change

The battery starts fully charged, so the initial percent charge \( P(0) = 100 \). The charge decreases by half a percent (or \( \frac{1}{2}\% \) or \( 0.5\% \)) per minute. In decimal form, \( 0.5\%=\frac{0.5}{100} = 0.005 \). Since it's a decrease, the rate of change is \( - 0.005 \) per minute.

Step2: Write the linear function

A linear function has the form \( P(t)=P_0 + rt \), where \( P_0 \) is the initial value, \( r \) is the rate of change, and \( t \) is the time. Substituting \( P_0 = 100 \) and \( r=- 0.005 \) (or \( r =-\frac{1}{200}\) since \( 0.005=\frac{1}{200}\)), we get:
\( P(t)=100-\frac{1}{200}t \) (or \( P(t) = 100-0.005t \))

Answer:

\( P(t)=100 - \frac{1}{200}t \) (or \( P(t)=100 - 0.005t \))