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Use the situation below to answer all parts of question 3.

A lake near the Arctic Circle is covered by a 3-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease by 0.75 meters each week.

Part 1

Identify the equation that represents this situation.

Responses

y = 0.75x + 3
y = 0.75x + 3

y = -0.75x + 3
y = -0.75x + 3

y = 3x + 0.75
y = 3x + 0.75

y = -3x + 0.75

1 answer

To represent the situation mathematically, we need to formulate an equation that describes how the thickness of the ice, \( y \), changes over time, represented by the number of weeks, \( x \).

Initially, the thickness of the ice is 3 meters. Each week, the ice melts by 0.75 meters, indicating a decrease in thickness over time.

Thus, the relationship can be described by the equation:

\[ y = -0.75x + 3 \]

Where:

  • \( y \) is the thickness of the ice remaining after \( x \) weeks,
  • 3 is the initial thickness of the ice,
  • \( -0.75 \) indicates that the thickness decreases by 0.75 meters each week.

So, the correct response is:

y = -0.75x + 3