Concept explainers
25–28 ■ Law of Cooling These exercises use Newton’s Law of Cooling.
Time of Death Newton’s Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is
(a) Find a function
(b) If the temperature of the body is now
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Algebra and Trigonometry (MindTap Course List)
- The Beer-Lambert Law As sunlight passes through the waters of lakes and oceans, thelight isabsorbed, and the deeper it penetrates, the more its intensity diminishes. The light intensityI at depth x is given by the Beer-Lambert Law: I=I0ekx Where I0 the light intensity at the surface and k isis a constant that depends on the murkiness of the water (see page 402). A biologist uses a photometer to investigate light penetration in a northern lake, obtaining the data in the table. (a) Use a graphing calculator to find an exponential function of the form given by the Beer-Lambert Law to model these data. What is the light intensity I0 at the surface on this day, and what is the “murkiness” constant kfor this lake?(Hint: if your calculator gives you a function of the form I=abx .convert this to the form you want using the identities bx=eIn(bx)=exInb . See Example 1(b).) (b) Make a scatter plot of the data, and graph the function that you found in part (a) on your scatter plot. (c) If the intensity drops below 0.15 lumen (lm) , a certain species of algae can’t survive because photosynthesis is impossible. Use your model from part (a) to determine the depth below which there is insufficient light to support this algae.arrow_forwardLaw of Cooling These exercise use Newton’s Law of Cooling. Cooling Soup A hot bowl or is served at a dinner party It Starts to according to Newton's Law Of Cooling, so its at time t is given by T(t)=65+145e0.05t where t is measured in minutes and T is measured in (a) What is the initial temperature Of the soup? (b) What is the after 10 min? (e) After how long will the temperature IO(YF?arrow_forward
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