Concept explainers
25–28 ■ Law of Cooling These exercises use Newton’s Law of Cooling.
Cooling Soup A hot bowl of soup is served at a dinner party. It starts to cool according to Newton’s Law of Cooling, so its temperature at time t is given by
where t is measured in minutes and T is measured in
(a) What is the initial temperature of the soup?
(b) What is the temperature after 10 min?
(c) After how long will the temperature be
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Algebra and Trigonometry (MindTap Course List)
- Law 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_forwardThe Beer-Lambert Law As sunlight passes through the waters of lakes and oceans, the light is absorbed, and the deeper it penetrates, the more its intensity diminishes. The light intensity I at depth x is given by the Beer-Lambert Law: I=I0ekx where I0 is the light intensity at the surface and k is 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. Light intensity decreases exponentially with depth. 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 k for 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=eln(bx)=exlnb. See Example 1b. Make a scatter plot of the data, and graph the function that you found in part a on your scatter plot. If the light intensity drops below 0.15 lumen lm, a certain species of algae cant 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. Depth ft Light intensity lm Depth ft Light intensity lm 5 10 15 20 13.0 7.6 4.5 2.7 25 30 35 40 1.8 1.1 0.5 0.3arrow_forwardCONCEPTS For an object in damped harmonic motion with initial amplitude a, and period 2/, and damping constant c find an equation that models the displacement y at any time t if a y=0 at time t=0: y= ____________. b y=a at time t=0: y= ____________.arrow_forward
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