Group D: Modeling (Applications) 1 a) To enter college at 18 years old with $50,000, how much money must be invested at birth. Assume investment at 4.5% annual interest compounded quarterly? (Accurate to nearest dollar.) b) What should be your annual rate of interest to double over 7 years an initial $10,000 investment compounded monthly ? (Accurate to nearest tenth of a percent.) 2) The population of Upper Podunk has grown exponentially from 15,000 people in 1990 to 25,000 people in 2000. a Determine an exponential model for the population (P), with the relative growth rate accurate to 4 decimal places. b) Based on this model, in what calendar year would the population reach 28,000 people? 3) A sample of a special atomic element decayed exponentially to 33% of its original mass after 8 days. a) Find the half-life of this element, accurate to the nearest day. b) Find the percentage of the original mass remaining after 12 days, accurate to the nearest percent.4) A football is thrown down a playing field. Its path (trajectory) is given by the equation y = -0.005x3+ x+ 5, where x is the distance the ball has traveled horizontally, and y is the height of the ball above ground level, both measured in feet. What is the maximum height attained by the ball above ground level? 5) The graph of the exponential function f(x) = ("" is shown below. Find the EXACT values of a and b. YA ( 4 ,3 ) X6) A rancher with 800 ft of fencing wants to enclose a rectangular area including three pens each with the same width. However the length of the second pen is twice the length ofthe first pen. And the length ofthe third pen is twice the length of the second pen. --L~ a) Determine the function that models the total area (A) of the three pens combined in terms of its width (W) only. b) Find the width (W) that provides the largest possible total area ofthe three pens combined. Group E: Miscellaneous 1) Based on log 5= 1.6and log 7= 2.2, determine EXACTLY each of the following: a) log 125 b) 108. V5 c) log Ta-3 2) Let P(x) = 2x101 - 3x2 + 4. a) Determine the remainder when P(x) is divided by x+1. b) Is (x+1) a factor of the function P? 3) If (x+2) is a factor of P(x) = x3 - 3x2 - 9x - 18, determine all zeros of P(x)