To calculate: The Summer Simmer Index S and the Apparent Temperature A for both the average daily maximum and the average daily minimum temperature. If the “feels like” temperature often reported in summer weather forecasts measures the combined effects of humidity and high temperatures. Two of the most common models used to determine this effect are the Summer Simmer Index (S) developed by John W. Pepi and the Apparent Temperature (A) developed by Robert Steadman. These models are given by
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Mathematical Applications for the Management, Life, and Social Sciences
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- The 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_forwardradioactive Decay These exercises use the population radioactive Decay. Radioactive Cesium The half-life of cesium- 37 is 30 years. Suppose we have a sample. (a) Find a function m(t)=m0et/k that mass remaining after t years. (b) Find a function m(t)=m0ert that models the remaining after t years. (c) How much of sample Will remain after 80 years? (d) After how many years will only 2 g of the sample remain?arrow_forwardA Population of Foxes A breeding group of foxes is introduced into a protected area, and the population growth follws a logistic pattern. After t years, the population of foxes is given by N=37.50.25+0.76t foxes. a. How many foxes were intorduced into the protected area? b. Make a graph of N versus t and explain in words how the populatoin of foxes increases with time. c. When will the fox population reach 100 individuals?arrow_forward
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