we have C'(0) = 3.7 billion and C'(7) = 3 billion

now we know C'(t) is linear, so let's find it's slope:

using (x1,y1) = (2000, 3.7 b) and (x2, y2) = (2007, 3 b)

m = change in C(t)/change in time

= (3b - 3.7b)/(2007 - 2000)

= 0.7/-7

= -1/10 billion/yr

so we have C'(t) = (-1/10)t + 3.7 billion .........where b is the y-intercept