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 0 ≤ x ≤ 50.†
Determine the value of x in the domain
0 ≤ x ≤ 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