Answer :
Answer: The required function formula is,
S(t) = 2 - 0.25 t
Step-by-step explanation:
Here, the initial thickness of the ice sheet = 2 meters,
After 3 weeks, the thickness of ice sheet = 1.25 meters
Total changes in the thickness in 3 weeks = 2 - 1.25 = 0.75 meters,
⇒ Total changes in the thickness in 1 weeks = 0.75/3 = 0.25 meters,
Since, the ice is melting with the constant rate.
⇒ The rate of ice decreasing = 0.25 meters per week.
⇒ Total changes in t weeks = 0.25 t meters
The new thickness of ice after t weeks = Initial thickness - Total changes in t weeks.
⇒ S(t) = 2 - 0.25 t
Which is the required function's formula.
We want to find an equation to model how the ice melts.
The wanted equation is:
S(t) = (-0.25 m/week)*t + 2m
We know that the ice melts at a constant rate, so we can describe the melting with a linear equation.
We know that at week 0, there is a 2 m thick sheet of ice.
3 weeks after, at week 3, the sheet is 1.25 m thick.
So we have two points, (0 weeks, 2m) and (3 weeks, 1.25m)
Now remember that a linear equation is given by:
S = a*t + b
where a is the slope and b is the y-intercept.
The slope is given by the quotient between the change in the y-value and the change in the x-value, so the slope is:
[tex]a = \frac{1.25 m - 2m}{3week - 0week} = -0.25 m/week[/tex]
Then the equation is something like:
S(t) = (-0.25 m/week)*t + b
To find the value of b we use the first point: (0 weeks, 2m)
Then we have b = 2m
The equation for the melting ice is given by:
S(t) = (-0.25 m/week)*t + 2m
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