The rate of spending on grants by foundations in the period of 1993-2003 was approximately s(t)=11+20/(1+1,800e^(-0.9t) billion dollars per year with t being the number of years since 1990 and (t being greater than or equal to 3 while also being less than of equal to 13). How can I estimate the total spending to the nearest $10 billion dollars on grants from 1998 to 2003?

Question

The rate of spending on grants by foundations in the period of 1993-2003 was approximately s(t)=11+20/(1+1,800e^(-0.9t) billion dollars per year with t being the number of years since 1990 and (t being greater than or equal to 3 while also being less than of equal to 13).  How can I estimate the total spending to the nearest $10 billion dollars on grants from 1998 to 2003?

oobleck · Answer

since s(t) is the rate of spending, the amount spent is just ∫ s(t) dt over the interval from t = 5 to 10

Anonymous · Answer

So I would just find ∫ [5,10] 11+20/(1+1,800e^(-0.9t)?

Anonymous · Answer

Why wouldn't the interval limits be the 3 and 13?

oobleck · Answer

because you didn't read the question carefully.