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A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.4 meters thick. Let y represent the ice sheet's thickness (in meters) after x weeks. Complete the equation for the relationship between the thickness and number of weeks. y=◻+ bar(+×)

A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 00.22 meters per week. After 77 weeks, the sheet is only 22.44 meters thick.\newlineLet y y represent the ice sheet's thickness (in meters) after x x weeks.\newlineComplete the equation for the relationship between the thickness and number of weeks.\newliney=□ y=\square

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Q. A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 00.22 meters per week. After 77 weeks, the sheet is only 22.44 meters thick.\newlineLet y y represent the ice sheet's thickness (in meters) after x x weeks.\newlineComplete the equation for the relationship between the thickness and number of weeks.\newliney=□ y=\square
  1. Find Initial Thickness: To find the initial thickness of the ice sheet before it started melting, we need to work backwards from the given information. \newlineWe know that after 77 weeks, the ice is 2.42.4 meters thick and it decreases by 0.20.2 meters each week. \newlineSo, we can calculate the initial thickness by adding 77 weeks' worth of melting to the final thickness.\newlineInitial thickness = 2.42.4 meters + (77 weeks ×\times 0.20.2 meters/week)
  2. Calculate Initial Thickness: Performing the calculation for the initial thickness:\newlineInitial thickness = 2.42.4 meters + (7×0.2(7 \times 0.2 meters)\newlineInitial thickness = 2.42.4 meters + 1.41.4 meters\newlineInitial thickness = 3.83.8 meters
  3. Write Equation Model: Now that we have the initial thickness, we can write the equation that models the relationship between the thickness of the ice sheet yy and the number of weeks xx. \newlineSince the ice is melting at a constant rate, the equation will be linear, in the form y=mx+by = mx + b, where mm is the rate of change and bb is the initial value.\newlineIn this case, mm is −0.2-0.2 (since the ice is decreasing by 0.20.2 meters each week), and bb is the initial thickness, which we found to be 3.83.8 meters.\newlineSo the equation is y=−0.2x+3.8y = -0.2x + 3.8.

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