Q: Let P(t) be the total output of a factory
Let P(t) be the total output of a factory assembly line after t hours of work. If the rate of production at time t is P’(t) = 60 + 2t – 1/4t2 units per hour, find the formula for P(t).
See AnswerQ: After t hours of operation, a coal mine is producing coal
After t hours of operation, a coal mine is producing coal at the rate of C ’(t) = 40 + 2t – 1/5 t2 tons of coal per hour. Find a formula for the total output of the coal mine after t hours of operati...
See AnswerQ: A package of frozen strawberries is taken from a freezer at -
A package of frozen strawberries is taken from a freezer at -5˚C into a room at 20˚C. At time t, the average temperature of the strawberries is increasing at the rate of T ‘(t) = 10e-0.4t degrees Cel...
See AnswerQ: Find all antiderivatives of each following function: f (x
Find all antiderivatives of each following function: f (x) = -4x
See AnswerQ: A flu epidemic hits a town. Let P(t)
A flu epidemic hits a town. Let P(t) be the number of persons sick with the flu at time t, where time is measured in days from the beginning of the epidemic and P(0) = 100. After t days, if the flu is...
See AnswerQ: A small tie shop finds that at a sales level of x
A small tie shop finds that at a sales level of x ties per day, its marginal profit is MP(x) dollars per tie, where MP(x) = 1.30 + .06x - .0018x2. Also, the shop will lose $95 per day at a sales level...
See AnswerQ: A soap manufacturer estimates that its marginal cost of producing soap powder
A soap manufacturer estimates that its marginal cost of producing soap powder is C ‘(x) = .2x + 100 dollars per ton at a production level of x tons per day. Fixed costs are $200 per day. Find the cos...
See AnswerQ: The United States has been consuming iron ore at the rate of
The United States has been consuming iron ore at the rate of R(t) million metric tons per year at time t, where t = 0 corresponds to 1980 and R(t) = 94e0.016t. Find a formula for the total U.S. consum...
See AnswerQ: Since 1987, the rate of production of natural gas in the
Since 1987, the rate of production of natural gas in the United States has been approximately R(t) quadrillion British thermal units per year at time t, with t = 0 corresponding to 1987 and R(t) = 17....
See AnswerQ: Drilling of an oil well has a fixed cost of $10
Drilling of an oil well has a fixed cost of $10,000 and a marginal cost of C ‘(x) = 1000 + 50x dollars per foot, where x is the depth in feet. Find the expression for C(x), the total cost of drilling...
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