## Related questions with answers

The Arctic Sea ice extent, the area of the sea covered by ice, grows seasonally over the winter months each year, typically from November to March, and is modeled by G(t), in millions of square kilometers, t months after November 1, 2014. (a) What is the sign of G'(t) for 0 < t < 4? (b) Suppose G''(t) < 0 for 0 < t < 4. What does this tell us about how the Arctic Sea ice extent grows? (c) Sketch a graph of G(t) for $0 \leq t \leq 4,$ given that G(0) = 10.3, G(4) = 14.4, and G'' is as in part (b). Label your axes, including units.

Solution

Verifieda) We know that if the derivative of a function is positive in an interval, then that function is increasing in that interval. In our case, we know that the area of the sea covered by ice increases from November to March, which means that $G'(t)$ must have a positive value for $0<t<4$.

b) If we draw the graph of the growth of the Arctic Sea ice extent in the interval $0<t<4$ (November to March), it will be concave down, since its second derivative is negative in this interval.

c)

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