# Thread: The number of Americans...

1. ## The number of Americans...

The number of Americans,in thousands who are expected to be over 100years old is approximated by n(t)=0.4018t^2+2.039t+50.71,where t is the year with t=0 corresponding to 1994.Determine the year that the number of Americans expected to be over 100 years old was increasing at a rate of 6000 people per year.

2. Originally Posted by mathcalculushelp
The number of Americans,in thousands who are expected to be over 100years old is approximated by n(t)=0.4018t^2+2.039t+50.71,where t is the year with t=0 corresponding to 1994.Determine the year that the number of Americans expected to be over 100 years old was increasing at a rate of 6000 people per year.
Take the derivative, set it equal to $\displaystyle 6$ (because the equation is per thousand people), and solve for $\displaystyle t$. You should get $\displaystyle t\approx4.93$, which implies that the year was around 1999.

3. find $\displaystyle n'(t) = 6$ and add 1994 to your answer.

Do you follow?