In the investigation of a homicide or accidental death, it is often important to estimate the time of death. from the experimental observations, it is known that the surface temperature of an object changes at a rate proportional to the difference between the temperature of the object and that of the surrounding environment or ambient temperature. this is known as newtons law of cooling. thus, if t(t) is the temperature of the object at time t, and ta is the constant ambient temperature: dt dt = k(t ta) where k > 0 is a constant of proportionality. suppose that at time t = 0 a corpse is discovered and its temperature is measured to be to. we assume that at the time of death, the body temperature td was at the normal value of 37 c. suppose that the temperature of the corpse when it was discovered was 29.5 c, and that two hours later, it is 23.5 c. the ambient temperature is 20 c. (a) determine k and the time of death. (b) solve the ode numerically and plot the results.

i think it would be 5

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

hope this !