SOLUTION: The number of Americans (in thousands) who are expected to be over 100 years old in year x is approximated by: F(x) = .27x2 + 3.52x + 51.78 where x= 0 corresponds to 2000 a

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Question 805876: The number of Americans (in thousands) who are expected to be over 100 years old in year x is approximated by:

F(x) = .27x2 + 3.52x + 51.78
where x= 0 corresponds to 2000 and the formula is valid through 2045.

a) Find a formula giving the rate of change in the number of Americans over 100 years old.
b) What is the rate of change in the number of Americans expected to be over 100 years old in the year 2015?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The numbers that come from that equation seem a bit too high, but I like them.

I assume this is a problem from calculus class, that you are expected to calculate the derivative of F%28x%29 , and that you know how to calculate derivatives of polynomials.

With those assumptions in mind,

a) dF%2Fdx=0.27%282x%29%2B3.25=0.54x%2B3.25

b) For the year 2015, x=15 and
dF%2Fdx=0.54%2A15%2B3.25=11.35
meaning that the number of centenarians would be increasing by 11,890 a year.