Calculus word problem (need help quick please!!)

Question

The divorce rate in the U.S. Is approximated by D(t)=100000e^0.025t where D(t) is the number of divorces occurring at time t and t is the number of years since 1900. Find the total number of divorces from 1900 to 2005.

Answer 1

We have the divorce rate, and we want the number of divorces, so we can integrate D(t) to get this. Since we start atn year 1900, t will be measured from 0 to 105.

 

So we have the integral of D(t) from 0 to 105.

 

∫100000e^(.025t)dt from 0 to 105 -->  =  100,000e^(.025t) / .025 = 4,000,000e^(.025t) from 0 to 105 

 

 

4,000,000e^(.025*105) - 4,000,000e^(0) = 5.12* 10^7