The U.S. Bureau of the Census prediction for the percentage of the population 65

Question

The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = -0.00022x3 + 0.014x2 - 0.0033x + 12.236 percent where x is the number of years since 2000, data from OS X s 50.+ Determine the value of x in the domain 0 sxs 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). Thus, in which year is the percentage is predicted to be increasing most rapidly? Calculate the percentage at that time. (Round your answer to two decimal places.) % Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.) percentage points per year

Explanation / Answer

given p(x)=-0.00022x3+0.014x2-0.0033x+12.236

=>p'(x)=-0.00066x2+0.028x-0.0033

=>p''(x)=-0.00132x+0.028

=>p'''(x)=-0.00132

percentage increases most rapidly when p''(x)=0, p"'(x)<0

=>-0.00132x+0.028=0

=>x=0.028/0.00132

=>x=700/33

=>x=21.212121212121212121212121212121

value of x is 21.212

In the year 2021 the percentage is predicted to be increasing moist rapidly

percentage at that time =p(700/33)

=>percentage at that time =-0.00022(700/33)3+0.014(700/33)2-0.0033(700/33)+12.236

=>percentage at that time =16.37 %

rate of change =p'(700/33)

=>rate of change =-0.00066(700/33)2+0.028(700/33)-0.0033

=>rate of change =0.294 percentage points per year

PLEASE RATE IF HELPFUL.PLEASE COMMENT IF YOU HAVE ANY DOUBT

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