Complete question :
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 at a constant rate. After four weeks, she is only 1.6 m thick. Let S(t) denote the ice sheet's thickness S (measured in meters) as a function of time t (measured in weeks). Write the function's formula
Answer:
S(t) = 3 - 0.3t
Explanation:
Given that:
Initial thickness = 3m
Assume the rate of decrease is constant
Thickness after 4 weeks = 1.6 m
To obtain a function for the scenario described above :
We can observe that the function is a linear function, given that rate of decrease per week is constant :
To obtain the rate of decrease :
Change after 4 weeks :
(Initial thickness - thickness after 4 weeks) / number of weeks
(3m - 1.6m) / 4
= 1.2m / 4
= 0.3 m per week
General form of a linear function :
y = mx + c
m = rate of change per unit
Hence, our function becomes ;
S(t) = 3 - 0.3t