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. 1. 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). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)

Newell et al. 2022 observed the following relationship between precipitation p (measured in mmrainfall) on the abundance of arthropods A (measured in mg/m2 biomass) in Peru. I provided an image of the equation below (a) On what intervals does increasing precipitation increase biomass? (b) On what intervals does increasing precipitation decrease biomass? c)At what rate does increasing precipitation increase/decrease biomass in a rain forest thatreceives 500mm of rain annually?

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Write an absolute value function f(t) to describe an individual variance from normal body temperature where t is the individual current temperature

Suppose the relationship between Y and X is given by: Y = 25 - 3X + error  By how much does the expected value of Y change if X decreases by 2 units?

It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:  x 5.75 6.75 7.75 8.50 9.25 y 27 16 46 62 95 ​ What percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line? Round your answer to the nearest tenth of a percent.    3.4%        18.4%        81.6%        9.7%