Maximum Oil Production It has been estimated that the total production of oil from a certain oil well is given by T(t) = -1000(t + 11)e-0.16 + 11,000
thousands of barrels t years after production has begun. Determine how many years after production has begun when the oil well will be producing at maximum capacity.
(Keep in mind this formula expresses the total of all production from time to time t, not the production at time t. Think about what you should maximize to arrive at the
answer.)
years after production has begun
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Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?