I need help with this question!

Q: Romina is an oceanographer who recently obtained ocean temperature and ocean density data from the Labrador Sea using an argo foat. Her colleague, Nico, however, goes scuba-diving to obtain data from only two depths. Nico measures a water temperature of 7 C at a depth of 50 meters and 3.6 C at a depth of 125 meters. This research group is collaborating with our MAT135 course to help them analyze their data.

Part 1:

(Two marks) Determine a linear mathematical model for the temperature, T (in degrees Celsius), as a function of depth, z (in meters) by fnding an equation of the secant line that goes between Nico's two data points.

Part 2:

(One mark) Nico asks us to predict the ocean temperature at the surface using his data. What value would you provide to Nico?

Part 3:

(Three marks) Romina delivers her data to a group of MAT135 students. The temperature, T (in degrees Celsius)

and density, (in kg/m3) profles are shown in the graphs below. Notice that Romina has used depth on the vertical axis. The horizontal axes are temperature (in the frst graph) and density (in the second graph). Using Depth on the vertical axis is the standard in oceanography since it mimics how we visualize the ocean (depth being vertical). We still think of temperature and density as functions of depth, here. Rotating your paper 90 degrees counter clockwise may help you visualize.

Depth (m) 250 500 750 H C O C 1250 1500 1750 2000 250 500 750 Depth (m) l-' O O D 1250 1500 1750 2000 ' . . I i r 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.? 0.8 Temperature ('C) Density (Kgfmjl +1.027e3 Note: There is a nearly vertical part of both graphs from depth 0 meters, to depth approximately 50 meters. (This is on purpose.) Consider the derivative nip/dz. Sketch a graph that shows Lip/dz on the vertical axis, and 2 on the horizontal axis. You should draw a rough sketch and exact values are NOT expected. However, try to capture the approximate locations of key features in the nip/dz graph. Again, rotating the graphs above 90 degrees counter clockwise may help you visualize