An electric vehicle's battery is being charged. The charge of the battery, C, as a percent… — SAT

An electric vehicle's battery is being charged. The charge of the battery, $C$ , as a percentage of its full capacity, $t$ minutes after the charging begins is modeled by the equation $C = 1.2t + 18$ , where $t \le 60$ . According to the model, what was the battery's charge percentage when the charging began?

Answer: 18 %

Answer

The battery's charge percentage when the charging began was 18.

The linear relationship is given by the equation

C = 1.2t + 18

. The constant term in this linear model, 18, represents the y-intercept, which is the value of

C

when

t = 0

. In the context of this scenario,

t = 0

represents the time when the charging began, and

C

represents the charge percentage. Substituting

t = 0

into the equation yields

C = 1.2(0) + 18 = 18

. Therefore, the battery's charge percentage was 18 when the charging began.

Step-by-Step Solution

Determine the value of the independent variable

t

when charging began.

t = 0

The initial state or the start of the charging process corresponds to a time of 0 minutes.

Substitute

t = 0

into the equation

C = 1.2t + 18

C = 18

Evaluating the linear equation at

t = 0

yields the constant term, representing the initial charge percentage.

Key Concept

Interpreting the y-intercept of a linear relationship in context

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