The average price paid by the synfuel industry for a short ton of coal between 2002 and 2005 can be modeled as P(t) 1.42- 6.1t33.5 dollars where t is the number of years since the beginning of 2000 (a) Use the limit definition of the derivative to develop a formula for the rate of change of the price of coal used by the synthetic fuel industry p'(t) 2.8t-6.1 dollars per year = (b) How quickly was the price of coal used by the synthetic fuel industry growing in the middle of 2005? 2.3 Xdollars per year The average price paid by the synfuel industry for a short ton of coal between 2002 and 2005 can be modeled as P(t) 1.4t2- 6.1t33.5 dollars where t is the number of years since the beginning of 2000 (a) Use the limit definition of the derivative to develop a formula for the rate of change of the price of coal used by the synthetic fuel industry. P'(t)= dollars per year (b) How quickly was the price of coal used by the synthetic fuel industry growing in the middle of 2005? X dollars per year 7.9

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