A company introduces a new product for which the number of units sold S is
       
      
                
     
    
    
    
    
    1 answer:
            
              
              
                
                
(a) The "average value" of a function over an interval [a,b] is defined to be 
(1/(b-a)) times the integral of f from the limits x= a to x = b. 
Now S = 200(5 - 9/(2+t)) 
The average value of S during the first year (from t = 0 months to t = 12 months) is then: 
(1/12) times the integral of 200(5 - 9/(2+t)) from t = 0 to t = 12 
or 200/12 times the integral of (5 - 9/(2+t)) from t= 0 to t = 12 
This equals 200/12 * (5t -9ln(2+t)) 
Evaluating this with the limits t= 0 to t = 12 gives: 
708.113 units., which is the average value of S(t) during the first year. 
(b). We need to find S'(t), and then equate this with the average value. 
Now S'(t) = 1800/(t+2)^2 
So you're left with solving 1800/(t+2)^2 = 708.113 
<span>I'll leave that to you</span>
                                
             
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The answer is -7! hope this helps