Modeling Using Function Notation Answers

The thread length of a screw is the part of the screw with threads. The function t(x) = |x – 63.75| can be used to find the difference, in millimeters, of a specific screw’s thread length, x, and the expected value. If a screw’s thread has a radius of 35.5 millimeters, the volume of the difference in thread can be calculated by the function V(t) = 1,260.25πt.

A flare is designed to follow the path modeled by the function h(t) = –16t2 + 100t, where t is the time elapsed, in seconds, and h(t) is the height, in feet, of the flare at that time. The function can be used to convert the height in feet to the height in meters.

An airplane’s average speed from San Diego to Dallas can be calculated using the function where t is the number of hours of travel. When there are tailwinds, the increased speed can be calculated using the functionw(s) = fs, where f is the percent increase as a decimal. On a given day, the tailwinds caused the average speed to increase by 2.5%, or w(s) = 1.025s.

Membership to a racket ball club has an application fee and a monthly fee that can be modeled by the function c(m) = 12.50m + 49, where m is the number of months of membership. The club is running a special in which the application fee is being waived as well as the first month’s payment. This can be modeled by the function s(c) = c – 12.50.

A ball is being inflated at a rate that can be modeled by the function V(t) = 10t, where t is the number of seconds spent inflating the ball. The radius at a given volume can be modeled by the function .Which composite function can be used to determine the radius of the ball depending on the number of seconds spent inflating the ball?

The function can be used to determine the side length, x, of a cube given the surface area of the cube, A. The function V(x) = x3 can be used to find the volume of a cube. How can these functions be combined?

A business plan is centered around a circular area of distribution. The plan calls for the radius of the distribution to increase 50 miles per year. The investors have asked that the plan include a reference to the area of distribution based on the number of years in business. These functions model this plan:Radius in y years: r(y) = 50y Total area: A(r) = πr2; r in miles

One brand of coffee is packaged in cylinders where the height is equal to the radius, r. The volume of the package, in cubic centimeters, can be found using the function V(r) = πr3. The number of ounces of coffee in the cylinder depends on the volume of the cylinder, V, in cubic centimeters. This can be modeled by the function C(V) = 3.2V.

A profit formula for dining plates from the previous year was modeled by the function P(d) = –15d2 + 1,200d – 2,000. The manufacturer noticed an increase in the number of units sold by 50% the next year, which can be modeled by the function l(d) = 1.5d.

A roller coaster starts with the cars being pulled up a ramp. The mass of the cars is estimated by the function m(p) = 175p + 1,180 where p is the number of passengers in the car. The potential energy of the car is calculated using the function E(m) = 9.8mh, where h is the height of the ramp.