A service station currently has 190 cases of motor oil. Over the next six months inventory of oil will be recorded monthly. Assume that the inventory is given by f(t)=190e^−0.4t, where t is the number of months from the present. Answer the following questions, rounding your answer to the nearest tenth.
a) How many cases of oil are there at the start of the six-month period?
b) How many cases of oil are left at the end of the six-month period?
c) What is the average number of cases in inventory over the six-month period?
(a) at the start, t=0 -- what is 190*e^0?
(b) f(6) = _____
(c) as usual, that would be
1/(6-0) ∫[0,6] f(t) dt = 1/6 ∫[0,6] 190e^(-0.4t) dt ≈ 72