# Math Help - 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 $6$ (because the equation is per thousand people), and solve for $t$. You should get $t\approx4.93$, which implies that the year was around 1999.

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

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