Oil production. Using production and geological data, the management of an oil company estimates...

Question

Oil production. Using production and geological data, the management of an oil company estimates that oil will be pumped from a producing field at a rate given by

where R(t) is the rate of production (in thousands of barrels per year) t years after pumping begins. Find the area between the graph of R and the t axis over the interval [5, 10] and interpret the results.

Robert · Accepted Answer

Answer  
Given  
Rate of oil pumping R(t)= [100/(t+10)] +10  
  
The required area with interval [5, 10] , will be  
  
R = 10∫5   {[100/(t+10)] +10} dt  
= 10∫5   [100/(t+10)] dt + 10∫5   10 dt  
=100 [In(t+10)]610  + [10t ]610  
= 100 ( In(20)-In (15))+ 10*5  
=100 In(20/15)+50  
=100*0.

Oil production. Using production and geological data, the management of an oil company estimates that oil will be pumped from a producing field at a rate given by where R(t) is the rate of production...

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