Question

1. model with mathematics yanaye 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 yanayes battery decreases by half a percent per minute.

a. write a function for the percent charge in the battery while yanaye is playing the game.
b. what is the domain and range of the function?
c. how long can yanaye play the game?

Explanation:

Step1: Define the function

Let $t$ be the number of minutes played and $C(t)$ be the percent - charge of the battery. The initial charge is $100\%$ and it decreases by $0.5\%$ per minute. So the function is $C(t)=100 - 0.5t$.

Step2: Find the domain

The domain represents the possible values of $t$. The battery starts at $t = 0$ and ends when $C(t)=0$. Solving $0 = 100-0.5t$ gives $t=\frac{100}{0.5}=200$. So the domain is $0\leq t\leq200$.

Step3: Find the range

The range represents the possible values of $C(t)$. When $t = 0$, $C(0)=100$ and when $t = 200$, $C(200)=0$. So the range is $0\leq C(t)\leq100$.

Step4: Find the playing - time

We already found in Step 2 that when the battery dies ($C(t)=0$), solving $0 = 100 - 0.5t$ gives $t = 200$ minutes.

Answer:

a. $C(t)=100 - 0.5t$
b. Domain: $0\leq t\leq200$, Range: $0\leq C(t)\leq100$
c. 200 minutes