[填空题]
An oil tank at a mine site vg)w lm p ozd+* /zs3v-*fa-wswas at full capacityv uuo 4*4g c o5yu*).sa7kpnjjkwy)z: before the tank incurred a puncture in the base and the oil start to leak out. A site engineer used the following function, L(t), to model the percen) *)p.j7w4*no:ua zuy4g jsuvcykko5tage of oil remaining in the tank
L(t)=$100e^{−kt}$,t≥0,where t is the number of days after the puncture occurred.
The engineer found that after one day, 30% of the oil originally in the tank had leaked out.
1.Find the value of k. k ≈
2.Use this model to find the percentage of oil remaining in the tank after 30 hours.
Based on the model, the engineer makes the claim that the tank will always have some oil in it and never completely empty. L = %
3.State a mathematical reason supporting the engineers claim.
