Data for the area of sea ice in the Arctic is obtained from satellite images. The rate of change of the area of Arctic sea ice (in millions of $\mathrm{km}^2 / \mathrm{yr}$ ) is shown in the table for the period 2003-2011. Use the Trapezoid Rule to estimate the net change in Arctic sea ice over this period. Interpret your answer.

Year	2003	2004	2006	2007	2009	2010	2011
Rate of change	0	-0.25	-0.65	-0.60	0.1	-0.40	-0.30

Using this plot of annual peak discharge, what is the probability each year that a flood of 1,000 cubic meters per second will occur?

A. 1 in 1,000 , or $0.01 \%$

B. 1 in 100 , or $1 \%$ (100-year flood)

C. between 10 and $20 \%$

D. more than $20 \%$

Draw and label a diagram showing the stages in the life cycle of a typical gymnosperm

Draw a diagram explaining the water cycle. Label the processes involved as biological or physical/chemical.

What is the term for the part of the hydrosphere that is frozen?

Give an example of the hydrosphere interacting with the geosphere.

During the water cycle, water evaporates, rises into the atmosphere, and eventually falls backs to Earth's surface as precipitation. What is the original source of energy that produces these changes?

A system consists of components of matter and energy and the processes that involve the matter and energy. Sort the items in the list as components of matter, energy, or processes in a system. a. chemical reaction, b. gas, c. heat, d. lava, e. light, f. melting, g. motion, h. rock, i. water.

Find the length of the following curves. y=ln x between x=1 and x=b>1 given that

$$\int \frac { \sqrt { x ^ { 2 } + h ^ { 2 } } } { x } d x = \sqrt { x ^ { 2 } + a ^ { 2 } } - a \ln \left( \frac { a + \sqrt { x ^ { 2 } + a ^ { 2 } } } { x } \right) + C$$

.

Which is greater? For the following regions R, determine which is greater: the volume of the solid generated when R is revolved about the x-axis or about the y-axis.

P is bounded by $y=4-2 x$, the $x$-axis, and the $y$-axis.

Find the length of the following curves.

$$y = x ^ { 3 } / 3 + x ^ { 2 } + x + 1 / ( 4 x + 4 )$$

on the interval [0, 4]

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=

$$x^2$$

, y=2-x, and x=0 in the first quadrant; revolved about the y-axis.

For the following regions R, determine which is greater—the volume of the solid generated when R is revolved about the x-axis or about the y-axis. R is bounded by y=4-2x, the x-axis, and the y-axis.

The population of an endangered species changes at a rate given by $P^{\prime}(t)=30-20 t$ (individuals/year). Assume the initial population of the species is 300 individuals, and $t$ is measured in years.
a. What is the population after 5 years?
b. When will the species become extinct?
c. How does the extinction time change if the initial population is 100 individuals? 400 individuals?