Find the function?

Question

National expenditures for health care (in billions of dollars) have risen dramatically since 1960 when the total was $26.7 billion. According to data from the US dept of HHS, the rate of change of expenditures can be modeled by h'(x)= 0.0126t^2+1.532t-5.08, where t=0 represents 1960. Find the function that models the expenditures for health care using the initial condition given to solve for c.

Answer 1

This is an integral problem. Integrate h'(x) to get h(x) = 0.0042t^3 + 0.766t^2 - 5.08t + C. And since you know h(0) = $26,700,000,000, you can easily solve for C.