Modeling Using Function Notation Answers

City planners anticipate an 8.2% population growth per year, including new residents and births. The population, in millions of people, based on this increase can be modeled by the function p(x) = 2.5(1.082)x, where x is the number of years of tracked growth. The planners also estimate a 3% population loss over the same time period that can be modeled by the function L(p) = p(0.97)x.

Boxes hold various numbers of square-based prisms in a single column. The square base of each prism has a side length of 18 inches. The height of each prism, h, can be found using the function , where V is the volume of the prism. The total height of the box, b, can be found using the function b(h) = xh, where x is the number of square-based prisms in a specific box.

The function r(x) = –0.000345(x – 50)2 + 2.1 can be used to model the curve of a road designed to allow for water to run off in rainstorms depending on the distance from the shoulder of the road, x, in feet. A European firm studying these curves is going to convert feet to meters using the function m(x) = 0.3048x.