The annual net income of General Electric for the period 2007-2011 could be approximated by P ( t ) = 1.6 t 2 − 15 t + 16 billion dollars ( 2 ≤ t ≤ 6 ), where t is time in years since the start of 2005 6 . According to the model, during what year in this period was General Electric's net income lowest? What was the corresponding net income? Would you trust model to continue to be valid long past this period? Why or why not?

Question

The annual net income of General Electric for the period 2007-2011 could be approximated by  P  (  t  )  =  1.6      t    2    −  15  t  +  16 billion dollars   (  2  ≤  t  ≤  6  ), where t is time in years since the start of       2005          6      . According to the model, during what year in this period was General Electric&#039;s net income lowest? What was the corresponding net income? Would you trust model to continue to be valid long past this period? Why or why not?

wijnvatid · Accepted Answer

Step 1  P  (  t  )  =  1.6      t    2    −  15  t  +  46  (  2  ≤  t  ≤  6  )      P    ′    (  t  )  =      d          d      t        (  1.6      t    2    −  15  t  +  46  )      P    ′    (  t  )  =  3.2  t  −  15Fpr net income; P&#039;t to be lowest (minimum),       P    ′    (  t  )  =  0 i.e.;  3.2  t  −  15  =  0  3.2  t  =  15  t  =      15    3.2    t  =  4.6875Hence, income won lowest in year:   (  2005  +  4.6875  )2009.68  ≈  2010i.e., net income lowest in the year 2010Step 2For net income,  P  (  t  )  =  1.6  (  4.6875      )    2    −  15  (  4.6875  )  +  46  =  10.84375 billion dollarsi.e. Corresponding net income is;10.84375 billion dollarNo this model can not be trusted for long past this period;because this model is good only when   2  ≤  t  ≤  6

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