Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. initially there were 5 million barrels of oil in the well; six years later 2,500,000 barrels remain.

a) at what rate was the amount of oil in the well decreasing when there were 3,000,000 barrels remaining?

b) when will there be 250,000 barrels remaining?

Using the decay law formula N=No x e^-kt
at  t=0,  No=5 million barrels
at  t= 6years,   N= 2,500,000 barrels=No/2

a) the rate is 5 millions - 3,000,000=2,000,000 barrels

b) let t this time
so N=No x e^-kt, implies  250,000=5,000,000,x e^-kt
25=500,x e^-kt,  5=100,x e^-kt, we must search for k,

at  t=0,  No=5 million barrels
at  t= 6years,   N= 2,500,000 barrels=No/2
so   N=No/2=No x e^-kt implies 1/2=e^-6k, so ln(1/2)= lne^ -6k, implies so 
-0.69= -6k and  k= 0.11
finally we can use N=No x e^-0.11t

250,000= 5,000,000  x e^-0.11t

1= 20 x e^-0.11t and 1/20= e^-011t,  0.05=e^-0.11t, ln(0.05)= - 0.11t
-3= -0.11t, so t = 27.22 years

pH = f(x) = -log₁₀x

1. Graphs

I used Excel to calculate the pH values and draw the graphs (see the Figure).

f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.

The points at which pH = 0 and pH = 1 are indicated by the large red dots.

2. x = 0.5

When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.

3. Transformations

(a) ƒ(x) = -log(x) + 1

This function has no y-intercept, because log(0) is undefined.

(b) ƒ(x +1) = -log(x + 1)

f(0) = -log(0 + 1) = -log(1) = 0

This function has a y-intercept at (0,0).

hope this helps please mark me brainliest!