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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=

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. Determine Initial Thickness: To find the equation that represents the relationship between the ice sheet's thickness (yy) and the number of weeks (xx), we need to determine the starting thickness of the ice before it began to melt. We know that the ice thickness decreases by 0.20.2 meters per week, and after 77 weeks, it is 2.42.4 meters thick.
  2. Calculate Total Decrease: We can calculate the initial thickness by adding the total decrease in thickness over 77 weeks to the final thickness. The total decrease is 77 weeks times 0.20.2 meters per week.\newlineTotal decrease = 77 weeks ×\times 0.20.2 meters/week = 1.41.4 meters.
  3. Find Initial Thickness: Now, we add the total decrease to the final thickness to find the initial thickness.\newlineInitial thickness = Final thickness + Total decrease = 2.42.4 meters + 1.41.4 meters = 3.83.8 meters.
  4. Write Equation: With the initial thickness found, we can write the equation that represents the relationship between the thickness yy and the number of weeks xx. Since the thickness decreases by 0.20.2 meters each week, the equation is:\newliney=Initial thickness−(Rate of decrease×Number of weeks)y = \text{Initial thickness} - (\text{Rate of decrease} \times \text{Number of weeks})\newliney=3.8 meters−0.2 meters/week×xy = 3.8 \text{ meters} - 0.2 \text{ meters/week} \times x

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