Question 67·Easy·Linear Functions
A video game's battery indicator estimates the remaining charge , in percent, with the model
where is the number of hours the game console has been used since it was fully charged, for . According to the model, what percent of battery charge remains after the console has been used for hours?
For linear function word problems like this, first identify what each variable represents and which one you’re given. Substitute the given value directly into the formula, then simplify step by step, being careful with order of operations (multiplication before subtraction). If the model tracks a quantity decreasing over time, ask yourself whether the expression you’ve computed represents what’s used or what’s remaining, and check that you’re answering exactly what the question asks.
Hints
Identify what you know and what you need
The equation tells you how battery percentage changes with time. You are told the console has been used for hours. Which variable in the equation does this correspond to?
Substitute before you calculate
Once you know which variable is , plug into the equation in place of that variable so you get a numerical expression for .
Do the operations in the right order
After substituting, there will be a subtraction and a multiplication. Compute the multiplication first, then subtract that result from 100.
Desmos Guide
Use Desmos to evaluate the expression
In Desmos, type the expression 100 - 4*18 into an expression line. The numerical value that Desmos returns is the remaining battery percentage after 18 hours, and you can match that value to the correct answer choice.
Step-by-step Explanation
Understand the model and the question
The equation gives the remaining battery percentage after hours of use. The question asks for the value of when the console has been used for hours, so here .
Substitute the given time into the equation
Replace with in the model:
Now we just need to simplify this expression.
Evaluate the expression to find the remaining battery
First compute the product . Then subtract this from 100:
So, according to the model, the battery has percent of its charge remaining after hours, which corresponds to answer choice C.