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110quiz6solutions

110quiz6solutions - Math 110 Quiz 6 Oct 26 2006 SOLUTIONS 1...

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Math 110 Quiz 6 Oct. 26, 2006 SOLUTIONS 1) The population of the southern United States can be closely approximated (to the nearest 0.01 million) by the exponential growth model A = Pe rt , where r = 0 . 0139 when t is measured in years and A is measured in millions. The population in 1940 was 41.67 million. (a) Determine a model for the population as a function of the number of years since 1940. (b) Use the function from part (a) to approximate the population in 1960 and in 1980. Solutions: (a) Using the model A = Pe rt , we see that A ( t ) = 41 . 67 ( e 0 . 0139 t ) (b) 1960 correponds to t = 20 and 1980 corresponds to t = 40. So, A (20) = 41 . 67 e 0 . 0139(20) 55 . 02 A (40) = 41 . 67 e 0 . 0139(40) 72 . 66 2) The dinosaur embryo freezer at a popular wild game park has been sabotaged. The freezer, initially at -10 degrees celsius, begins to warm to the room temperature of 25 degrees celsius. The rate of change r is - 0 . 16 when t is measured in hours. The embryos will be unusable once their temperature becomes 17 degrees celsius.
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