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Chapter 0: Problem 12

According to a study conducted in 2003 , the total number of U.S. jobs (in millions) that were projected to leave the country by year \(t\), where \(t=0\) corresponds to 2000 , is $$N(t)=0.0018425(t+5)^{2.5} \quad 0 \leq t \leq 15$$ How many jobs were projected to be outsourced in \(2005 ?\) In \(2010 ?\)

Short Answer

Expert verified
In 2005, approximately 0.92 million jobs were projected to be outsourced, and in 2010, approximately 3.23 million jobs were projected to be outsourced.

Step by step solution

01

Find the number of jobs outsourced in 2005

To find the number of jobs projected to be outsourced in 2005, let's first determine the value of \(t\) for 2005. Since \(t=0\) corresponds to the year 2000, we can find the value for 2005 by adding 5 to the year 2000, \(t=2005-2000 = 5\). Plug in this value into the function \(N(t)\): \[ N(5) = 0.0018425(5+5)^{2.5} \]
02

Calculate N(5)

Now we just need to calculate the value of \(N(5)\): \[ N(5) = 0.0018425(10)^{2.5} \approx 0.92 \] So, in 2005, approximately 0.92 million jobs were projected to be outsourced.
03

Find the number of jobs outsourced in 2010

Similarly, to find the number of jobs projected to be outsourced in 2010, we need to determine the value of \(t\) for 2010. As before, \(t=0\) corresponds to the year 2000, so for 2010, we get \(t=2010-2000 = 10\). Plug in this value into the function \(N(t)\): \[ N(10) = 0.0018425(10+5)^{2.5} \]
04

Calculate N(10)

Now we just need to calculate the value of \(N(10)\): \[ N(10) = 0.0018425(15)^{2.5} \approx 3.23 \] So, in 2010, approximately 3.23 million jobs were projected to be outsourced.

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Most popular questions from this chapter

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