(1)Geologists date geologic events by examining sedimentary layers in the ocean floors. For instance, they can tell when an ancient volcano erupted by noting where in the sedimentary layers its ash was deposited. This is possible because the rate of sedimentation is assumed to be largely constant over geologic eras, so the depth of the sedimentation is modeled by a linear function of time. To examine sedimentary strata, core samples (often many meters long) are drilled from the ocean floor, then brought to the laboratory for study. Special features in the layers, including the chemical composition of the deposits, can indicate climate change or other geologic events. It is estimated that the rate of sedimentation in a lake is 0.26 cm per year. The depth beneath the lake bottom at which a layer of sediment lies is a function of the time elapsed since it was deposited.

(a) Find a linear function that models the depth of sediment as a function of time elapsed.

(b) To what depth must we drill to reach sediment that was deposited 300 years ago?

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(2)The amount of trash in a county landfill is modeled by the function

T(x) = 34,800 + 6x

where x is the number of days since January 1, 1996, and T(x) is measured in thousands of tons.

(c) At what rate is the landfill receiving trash?