# Thread: Application problem involving indefinite integrals

1. ## Application problem involving indefinite integrals

Wite C(t) for the amount the U.S. military spent on personel in year t, where t is measured in years since 2000. The rate of increase of C(t) was about $3.7 billion per year in 2000 and was projected to decrease to$3 billion per year in 2007.

Find a linear model for the rate of change C'(t)

2. Originally Posted by Kenneth
Wite C(t) for the amount the U.S. military spent on personel in year t, where t is measured in years since 2000. The rate of increase of C(t) was about $3.7 billion per year in 2000 and was projected to decrease to$3 billion per year in 2007.

Find a linear model for the rate of change C'(t)
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