An oil refinery produces oil at a variable rate given by the following equation, where t is measured in days and Q is measure in barrels. Q'(t) = egin{cases} 700 & ext{if } 0 le t < 30 \ 2800 - 40t & ext{if } 30 le t < 40 \ 200 & ext{if } t ge 40 end{cases} a. How many barrels are produced in the first 35 days? b. How many barrels are produced in the first 50 days? c. Without using calculus, determine the number of barrels produced over the interval [70,90]. a. The oil refinery produced 28,500 barrels in the first 35 days. b. The oil refinery produced 37000 barrels in the first 50 days. c. The oil refinery produced 4000 barrels over the interval [70,90].
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For the first 30 days, the refinery produces oil at a rate of 700 barrels per day. So, in 30 days, it produces 30 * 700 = 21,000 barrels. For the next 5 days (from day 30 to day 35), the rate of production changes. We can calculate the total production for each Show more…
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