Question

A new oil field has just begun production. The first oil removed is the easiest to get out, and so production falls as time goes on. The instantaneous rate at which oil can be extracted is 14% of the amount of oil remaining per year. Here, "instantaneous" refers to the fact that as soon as any oil is removed, the rate of production falls proportionally in the "next" instant. If the company continues to extract oil at that instantaneous rate, when will the amount of oil left in the field first be less than 22 percent of the original amount?

Answer 1

.86=e^-k
k=-ln.86

.78=e^-kt
t= -ln.78 /k= ln.78 / ln.88

Answer 2

^ Answer above is not working

Answer 3

sine the rate of decrease is 14% of the amount present,

dp/dt = -.14p
dp/p = -.14 dt
lnp = -.14t + c
p = c e^-.14t

here, c is the original amount

when is only .22 left?

e^-.14t = .22
-.14t = ln.22
t = ln.22/-.14 = 10.8 years