According to a study conducted in 2003, the total number of U.S. jobs that are p
ID: 2961600 • Letter: A
Question
According to a study conducted in 2003, the total number of U.S. jobs that are projected to leave the country by year t, where t = 0 corresponds to 2000, is represented by the following function where N(t) is measured in millions.
How fast was the number of U.S. jobs that are outsourced changing in 2005? How fast will the number of U.S. jobs that are outsourced be changing at the beginning of 2015 (t = 15)? (Round your answers to the nearest whole number.)
According to a study conducted in 2003, the total number of U.S. jobs that are projected to leave the country by year t, where t = 0 corresponds to 2000, is represented by the following function where N(t) is measured in millions. N(t) = 0.0018425(t + 4)4.5 (0 t 15) How fast was the number of U.S. jobs that are outsourced changing in 2005? How fast will the number of U.S. jobs that are outsourced be changing at the beginning of 2015 (t = 15)? (Round your answers to the nearest whole number.)
Explanation / Answer
N(t) = 0.0018425(t + 4)^4.5
How fast was the number of U.S. jobs that are outsourced changing in 2005 ?
change of number of jobs obtained by taking derivative thus
N'(t) = 4.5*0.018425(t+4)^(4.5-1) = 0.0829125(t+4)^(3.5)
since t = 0 corresponds to 2000 t = 5 corresponds to 2005 thus
N'(t) = 0.0829125(t+4)^(3.5) = 0.0829125(5+4)^(3.5) = 181.3296375
N'(5) = 181 million jobs / year
How fast was the number of U.S. jobs that are outsourced changing in 2005 = 181 million jobs / year
How fast was the number of U.S. jobs that are outsourced changing in 2015 ?
N'(t) = 4.5*0.018425(t+4)^(4.5-1) = 0.0829125(t+4)^(3.5)
since t = 0 corresponds to 2000 t = 15 corresponds to 2015 thus
N'(t) = 0.0829125(t+4)^(3.5) = 0.0829125(15+4)^(3.5) = 2478.8920441736721018
How fast was the number of U.S. jobs that are outsourced changing in 2015 = 2479 million jobs / year
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