Question

Suppose that in 1970, there were 1.3 million college degrees awarded. This number increased to 2.5 million in 2010.

(a) Find a linear function D that approximates degree.
numbers in millions of years after 1970.
(b) Interpret the y-intercept on the graph of D.
(c) Estimate symbolically when this number was 2.2 million.
(a) D(x) =
(Use integers or decimals for any numbers in the expression.)

Answer 1

To find a linear function that approximates degree numbers in millions of years after 1970, we can use the slope-intercept form of a linear equation. The linear function is D(x) = 0.012x - 22.6.

Step-by-step explanation:

To find a linear function that approximates degree numbers in millions of years after 1970, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

We are given two points: (1970, 1.3) and (2010, 2.5). We can use these points to find the slope, which is the change in y divided by the change in x.

Slope (m) = (2.5 - 1.3) / (2010 - 1970) = 0.012 million per year

To find the y-intercept (b), we can substitute one of the points into the equation and solve for b:

1.3 = 0.012 * 1970 + b

b = 1.3 - (0.012 * 1970) = -22.6

So the linear function that approximates degree numbers after 1970 is D(x) = 0.012x - 22.6.