A lake near the Arctic Circle is covered by a 2-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 at a constant rate. After 3 weeks, the sheet is only 1.25 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.
Answer:
y = 2 - 0.25x
Step-by-step explanation:
From the question, the initial thickness of the ice sheet = 2 meters,
After 3 weeks, the thickness of ice sheet reduced to 1.25 meters
Hence, the difference in the thickness in 3 weeks is calculated as:
2m - 1.25m = 0.75m
The amount of changes that occurred in 3 weeks is given as:
= 0.75/3 = 0.25 meters,
We are told that, the ice is melting with the constant rate.
Therefore, the equation for the relationship between the thickness and number of weeks is given as:
y = 2 - 0.25x
<u>Answer</u>
1st solution: a = 1
b = 3
2nd solution: a = 2
b = 6
<u>Explanation</u>
1st solution
<em> 1</em>
<em> 333</em>
<em> 333</em>
<em> 333</em>
<em> </em><em><u> +333</u></em>
<em> </em><em><u> 1333</u></em>
2nd solution
<em> 2</em>
<em> 666</em>
<em> 666</em>
<em> 666</em>
<em><u> + 666</u></em>
<em><u> 2666</u></em>
