# The marrige rate (marriages per year) in the U.S. has been declining recently, w/ about 2e^-0.038t million marriages per year, where t is the number of years since 2010. Assuming that this rate...

The marrige rate (marriages per year) in the U.S. has been declining recently, w/ about 2e^-0.038t million marriages per year, where t is the number of years since 2010. Assuming that this rate continues, find the total number of marriages in the U.S. from 2010 - 2020

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### 1 Answer

The number of marriages per year is declining at `2*e^(-0.038*t) ` million where t is the number of years since 2010.

If the number of marriages in 2010 was X, `(dX)/dt = 2*e^(-0.038*t) ` where t is number of years since 2010.

`(dX)/(dt) = 2*e^(-0.038*t)`

`int_(X_2010)^(X_2020) dX = int_1^10 2*e^(-0.038*t) dt`

`~~` 14.676 million

**The number of marriages in the given period is 14.676 million**