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)= _____?

(b) Using your model, in what year will the number of desktop publishing jobs first exceed 61,000? _______

Using the point-slope form of the line,

y-39000 = (64/39)(x-2000)

So, when is y > 61000?

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

(a) We have two data points: (2000, 39,000) and (2010, 64,000).
Let's use the formula for a linear function, y = mx + b, where y represents the number of desktop publishing jobs and x represents the year.

We can start by finding the slope (m) using the formula m = (y2 - y1) / (x2 - x1).
m = (64,000 - 39,000) / (2010 - 2000) = 25,000 / 10 = 2,500.

Now, we can substitute one of the data points into the formula to find the y-intercept (b). Let's use the point (2000, 39,000).
39,000 = 2,500 * 2000 + b
39,000 = 5,000,000 + b
b = 39,000 - 5,000,000
b = -4,961,000.

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

(b) Now, we can use the linear function N(t) = 2,500t - 4,961,000 to find in what year the number of desktop publishing jobs first exceeds 61,000.

We need to solve the equation 61,000 = 2,500t - 4,961,000 for t.
2,500t = 4,961,000 + 61,000
2,500t = 5,022,000
t = 5,022,000 / 2,500
t ≈ 2,008.8.

Since the year cannot be fractional, we round up to the next whole year.
Therefore, the number of desktop publishing jobs will first exceed 61,000 in the year 2009.