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? ____
To find the number of desktop publishing jobs as a linear function of the year, we can use the two data points given: 39,000 jobs in 2000 and 64,000 jobs in 2010.
(a) To find the linear function, we need to determine the slope (m) and the y-intercept (b) of the equation y = mx + b, where y represents the number of desktop publishing jobs and x represents the year.
First, let's find the slope (m):
m = (change in y) / (change in x) = (64,000 - 39,000) / (2010 - 2000) = 25,000 / 10 = 2,500
Next, let's find the y-intercept (b):
Using the point (x, y) = (2000, 39,000) in the equation y = mx + b:
39,000 = 2,500 * 2000 + b
39,000 = 5,000,000 + b
b = 39,000 - 5,000,000
b = -4,961,000
Now, we can substitute the values of m and b into the equation to find N(t) - the number of desktop publishing jobs as a function of the year:
N(t) = 2,500t - 4,961,000
(b) To find the year when the number of desktop publishing jobs first exceeds 61,000, we can set N(t) to 61,000 and solve for t:
61,000 = 2,500t - 4,961,000
2,500t = 61,000 + 4,961,000
2,500t = 5,022,000
t = 5,022,000 / 2,500
t ≈ 2008.88
Therefore, the number of desktop publishing jobs first exceeds 61,000 in the year 2009.