Math191_Week7_section - over a period of time - increases...

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Math 191 Problem Set for Week 7 Section 1. Find the area of the region between the curve y = 2 1 - x and the interval - 1 x 1 . 2. Find the global maximum of f ( x ) = x 1 /x in the domain x > 0 . 3. A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 2 hours there are 10 , 000 bacteria. At the end of 5 hours there are 70 , 000 . How many bacteria were present initially? 4. Suppose the rate at which a rumor spreads - that is, the number of people who have heard the rumor
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Unformatted text preview: over a period of time - increases with the number of people who have heard it. If y is the number of people who have heard the rumor, then dy dt = ky, where t is the time in days. a. If y is 1 when t = 0 and y is 5 when t = 2 , nd k . b. Using the value of k from (a), nd y when t = 3 . 5. Prove or disprove: a. x-2 3 x grows slower than x 2 x . b. log 2 3 x 2 grows at the same rate as ( x + 7) 2 . 1...
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