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A government agency estimates the number of young adults (ages 18 to 24) in a particular country to be 31,000 (in thousands) in 2010 and changing at the rate of −x2 + 90x − 200 thousand per year, where x is the number of years since 2010. Find a formula for the size of this population at any time x. [Hint: Keep all calculations in units of thousands.]

User Onik
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1 Answer

3 votes

Answer:


\mathbf{L(x)= ( - (1)/(3))x^3 + 45x^2 -200x +31000}

Explanation:

From the given information:

Let assume the population is denoted by L

The rate of change of the young adults per year given can be represented as;


(dL)/(dx)= -x^2 +90x - 200

where;

x = 0 since 2010


dL = -x^2 +90x -200 dx


L = \int( -x^2 +90x -200 ) \ dx


L = - (1)/(3)x^3 + 45x^2 -200x +C

here;

L(0) = 31000


- (1)/(3)(0)^3 + 45(0)^2 -200(0)+C= 31000

C = 31000


\mathbf{L(x)= ( - (1)/(3))x^3 + 45x^2 -200x +31000}

User Ifconfig
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