Suppose that an oil spill in a lake covers a circular area and that the radius...

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Suppose that an oil spill in a lake covers a circular area and that the radius of the circle is increasing according to the formula r = f(t) = 12 + 1.65, where t represents the number of hours since the spill was first observed and the radius r is measured in meters. (Thus when the spill was first discovered, t = 0 hr, and the initial radius was r = f(0) = 12 + 01.65 = 12 m.) (a) Let A(r) = ², as in Example 5. Compute a table of values for the composite function A of with t running from 0 to 5 in increments of 0.5. (Round each output to the nearest integer.) Then use the table to answer the questions that follow in parts (b) through (d). 0.5 1.5 2.5 3 3.5 4 t A 0 2 (b) After one hour, what is the area of the spill (rounded to the nearest 10 m²)? m² (c) Initially, what was the area of the spill (when t = 0)? m² Approximately how many hours does it take for this area to double? hr 4.5 (d) Compute the average rate of change of the area of the spill from t = 0 to t = 2.5. (Round your answer to one decimal place.) m²/hr Over which of the two intervals is the area increasing faster? Ot=0 to t = 2.5 Ot= 2.5 to t= 5 OF 5 Compute the average rate of change of the area of the spill from t = 2.5 to t = 5. (Round your answer to one decimal place.) m²/hr ENG 8:10 PM Suppose that an oil spill in a lake covers a circular area and that the radius of the circle is increasing according to the formula r = f(t) = 12 + 1.65, where t represents the number of hours since the spill was first observed and the radius r is measured in meters. (Thus when the spill was first discovered, t = 0 hr, and the initial radius was r = f(0) = 12 + 01.65 = 12 m.) (a) Let A(r) = ², as in Example 5. Compute a table of values for the composite function A of with t running from 0 to 5 in increments of 0.5. (Round each output to the nearest integer.) Then use the table to answer the questions that follow in parts (b) through (d). 0.5 1.5 2.5 3 3.5 4 t A 0 2 (b) After one hour, what is the area of the spill (rounded to the nearest 10 m²)? m² (c) Initially, what was the area of the spill (when t = 0)? m² Approximately how many hours does it take for this area to double? hr 4.5 (d) Compute the average rate of change of the area of the spill from t = 0 to t = 2.5. (Round your answer to one decimal place.) m²/hr Over which of the two intervals is the area increasing faster? Ot=0 to t = 2.5 Ot= 2.5 to t= 5 OF 5 Compute the average rate of change of the area of the spill from t = 2.5 to t = 5. (Round your answer to one decimal place.) m²/hr ENG 8:10 PM

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SOLUTION a Using the formula Ar pi r2 we can compute the values of the composite function Aft for t ... View the full answer