Questions: Raw cake batter starts at a thickness of 2 centimeters in a pan but grows at 0.15 centimeters every minute in the oven. How tall will the cake be after a certain number of minutes?

Raw cake batter starts at a thickness of 2 centimeters in a pan but grows at 0.15 centimeters every minute in the oven. How tall will the cake be after a certain number of minutes?

Solution

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Solution Steps

Step 1: Identify the initial thickness of the cake batter

The initial thickness of the cake batter is given as 2 centimeters. This is the starting point before any growth occurs.

Step 2: Determine the growth rate of the cake batter

The cake batter grows at a rate of 0.15 centimeters every minute. This is the slope of the linear equation that describes the growth of the cake over time.

Step 3: Formulate the linear equation

The height of the cake \( y \) after \( x \) minutes can be expressed as: \[ y = 0.15x + 2 \] Here, \( 0.15x \) represents the growth over \( x \) minutes, and \( 2 \) is the initial thickness.

Final Answer

\(\boxed{y = 0.15x + 2}\)

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