Chapter 3 Quiz. Show all work for full credit. If using a calculator outline the steps that you used to find your answers.
- A rancher wants to enclose a rectangular corral. To save fencing costs, a river is used along one side of the corral and the other 3 sides are by 3,000 feet of fence. Assume that x represents the width (in feet) of 2 of the fenced sides, y the length (in feet) of the third fenced side and A is the area of the corral. Express the area A as a function of x. Find the dimensions of the corral that enclose the maximum area. What is the maximum area? Graph the area function.
- The US Census Bureau has projected the population of the US for the years from 2010 thru 2100, according to the data table below. Plot a scattergram of the data. Fit a quadratic function to the data and express the function of the population P as a function of time t (can use EXCEL’s ADD TRENDLINE as we did in class). Draw the best fitting curve on the scattergram. Use this regression model to predict the populations in the years 2015, 2075, and 2110. Round off your answers to the nearest thousand.
Year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
T 0 10 20 30 40 50 60 70 80 90
P 299862 324927 351070 377350 403687 432011 463639 497830 533605 570954
P IS IN THOUSANDS.
- The sum of the height y (in cms) and the base x (in cms) of a triangle is 24 cms. Express the area of a triangle as a function of x. Find the base that produces the maximum area of the triangle. What is the maximum area. Remember A = (1/2)Altitude times Base.
- Graph and find the zeros of the following polynomial functions. A) f(x) = 4x3 – 9x2 -8x -3 B) g(x) = x4 -8x.
- For the following two rational functions do the following. A) Locate vertical asymptotes and holes; B) Find the intercepts; C) Locate any horizontal asymptotes; D) Check for slant asymptotes and provide the equation of any slant asymptotes; E) graph each rational function and F) state the range and domain..
(1) F(x) = (3x2+17)/(x+5) (2) g(x) = (2x3 + x)/(x2 – 2x + 3)