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):Let Q(t) be the number of barrels left in the well after t years, measured in millions. Write a differential equation for Q that captures the information in the problem. Use k>0 for any proportionality constant you need. Be careful about signs.

Q'=

(B):Solve the above differential equation, without yet determining k.

Q(t)=

(C):Determine k.

k=

(D):At what rate was the amount of oil in the well decreasing when there were 3,000,000 barrels remaining? [Hint: Use the equation in (a). Be careful about units.]

rate= barrels/year

(E):When will there be 250,000 barrels remaining?

years=

Step-by-step explanation:

From the information we find that

Q'(t) = kQ(t)

with Q(0) = 5 and Q(6) = 2.5 in millions

A) Separate the variables and solve the DE

Using Q(0) = 5

A =5

B)

C)

Using Q(6) = 2.5

D) Use Q'(t) = -0.1155 (3) = -0.3465

Rate = -346500 barrels

(negative indicates decrease in number of barrels_

E) When Q = 250000 we have

After 26 years

( ͡° ͜ʖ ͡° ) copy and   paste it

step-by-step explanation:

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

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