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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 0.20.2 meters per week. After 77 weeks, the sheet is only 2.42.4 meters thick.\newlineLet yy represent the ice sheet's thickness (in meters) after xx 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 0.20.2 meters per week. After 77 weeks, the sheet is only 2.42.4 meters thick.\newlineLet yy represent the ice sheet's thickness (in meters) after xx weeks.\newlineComplete the equation for the relationship between the thickness and number of weeks.\newliney=□y=\square
  1. Rephrasing the Equation: Let's first rephrase the ＂What is the equation that models the relationship between the thickness of the ice sheet and the number of weeks?＂
  2. Calculating Initial Thickness: To find the initial thickness of the ice sheet before it started melting, we need to work backwards from the given information. We know that after 77 weeks, the ice is 2.42.4 meters thick and it decreases by 0.20.2 meters each week. So, we can calculate the initial thickness by adding 77 weeks' worth of melting to the final thickness.\newlineInitial thickness == Final thickness ++ (Rate of melting per week ∗* Number of weeks)\newlineInitial thickness =2.4= 2.4 meters ++ (0.20.2 meters/week ∗* 77 weeks)
  3. Performing Calculation: Performing the calculation for the initial thickness:\newlineInitial thickness = 2.4 meters+1.4 meters2.4\,\text{meters} + 1.4\,\text{meters}\newlineInitial thickness = 3.8 meters3.8\,\text{meters}\newlineThis is the value of 'aa' in the equation y=a−bxy = a - bx, where 'bb' is the rate of melting per week, and 'xx' is the number of weeks.
  4. Writing the Equation: Now we can write the equation using the initial thickness aa as 3.83.8 meters and the rate of melting bb as 0.20.2 meters per week. The equation will model the thickness yy of the ice sheet after xx weeks.\newliney=a−bxy = a - bx\newliney=3.8−0.2xy = 3.8 - 0.2x

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