There were 39,000 desktop publishing jobs in the United States in 2000. It has been projected that there will be 64,000 desktop publishing jobs in 2010.

(a) Using the BLS data, find the number of desktop publishing jobs as a linear function of the year.
N(t)=_____

To find the number of desktop publishing jobs as a linear function of the year, we can use the given data points from 2000 and 2010.

Let's assume that the number of desktop publishing jobs is a linear function of the year, denoted by N(t), where t represents the year.

We are given that in 2000, there were 39,000 desktop publishing jobs, which can be written as N(2000) = 39,000.

We are also given that in 2010, there will be 64,000 desktop publishing jobs, which can be written as N(2010) = 64,000.

Since we assume that N(t) is a linear function, we can use the point-slope form of a linear equation:
N(t) - N(2000) = m(t - 2000),

where m represents the slope of the line.

To find the slope (m), we can use the formula:
m = (N(2010) - N(2000)) / (2010 - 2000).

Substituting the given values, we have:
m = (64,000 - 39,000) / (2010 - 2000).

Simplifying this equation, we get:
m = 25,000 / 10 = 2,500.

Now, we can substitute the values of N(2000) = 39,000 and m = 2,500 into the point-slope form equation to get the linear function:

N(t) - 39,000 = 2,500(t - 2000).

We can simplify this equation further:
N(t) - 39,000 = 2,500t - 5,000,000.

Now solve for N(t):
N(t) = 2,500t - 5,000,000 + 39,000.

N(t) = 2,500t - 4,961,000.

Therefore, the linear function representing the number of desktop publishing jobs as a function of the year is:
N(t) = 2,500t - 4,961,000.