# The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled asp(x)0.00022x30.014x2- 0.0033x 12.236 percentwhere x is the number of years since 2000, data from 0 s x s 50.tDetermine the value of x in the domain 0x s 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

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Asked Nov 19, 2019
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Step 1

First of all, differentiate p(x) w.r.t. x and get p '(x).

A derivative of a function shows the increasing or decreasing nature of the function.

Step 2

Now, again differentiate p '(x) w.r.t. x to get p '' (x) and equate it to 0 to get the critical points.

The critical point is at x = 21.212

Step 3

Then find the value of p '' (x) at the critical point i.e. x = 21.212.

The value of p '' (x) at the critical point is 0.00000016 and...

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