At the start of 2008 the value of subprime mortgage debt outstanding in the United States was about $1,300 billion, was increasing at a rate of 40 billion dollars per year, but was decelerating at 20 billion dollars per year per year.

Question

At the start of 2008 the value of subprime mortgage debt outstanding in the United States was about $1,300 billion, was increasing at a rate of 40 billion dollars per year, but was decelerating at 20 billion dollars per year per year.
a. Find an expression for the rate of change (velocity) of the value of subprime mortgage debt at time t in years since the start of 2008.
b. Use the result of part (a) to find an expression for the value of subprime mortgage debt at time t, and use it to estimate the value at the start of 2009.

mathhelper · Accepted Answer

"...decelerating at 20 billion dollars per year per year"
----> a = -20 B$/year^2
rate of change of debt = -20t + c , where t is in years

when t = 0 (letting 2008 correspond with t = 0)
40 = -20(0) + c
c = 40

rate of change of debt = -20t + 40

debt = -10t^2 + 40t + k
when t = 0 , (2008), debt = 1300 B$
1300 = -10(0) + 40(0) + k
k = 1300

so debt = -10t^2 + 40t + 1300, where debt is in million dollars.

since 2009 would be like t = 1
debt in 2009 = -10(1) + 40(1) + 1300
= 1330 Billion dollars