BRIEF ANSWERS TO TEST 3 FOR COLLEGE ALGEBRA STUDENTS

• • y = P(x) has three x-intercepts (at x = -3, -1/2, 2), a y-intercept (at x = -6), two turning points, decreases to -infinity as x goes to -infinity, while it increases to +infinity as x goes to +infinity.
  • x is in (-infinity,-3] union [-1/2,2]
• • y-intercept at y=-2, x-intercepts at x = +/-2, vertical asymptote at x = -1, oblique asymptote y = (1/2)x - (1/2).
  • x is in (-2,-1) union (2,infinity)
• • x = 3 or -1
  • x = e^(square_root(2)) or e^(-square_root(2))
• • x = (-1/4)*ln(2/21)
  • x = ln(1+square_root(2))
• t = ln(2)/(.04) = about 17.33 years
• half life is h = -20/log_2(.7) = about 38.87 years, so it will take t = -h*log_2(.6) = 28.64 years until it has decayed to 60 percent. Answer: 8.64 more years until it has decayed to 60 percent.
• An investment that increases by a factor of n every n years increases by a factor of n^(1/n) every year. Since 2^(1/2) = 1.414..., 3^(1/3) = 1.442..., and 4^(1/4) = 1.414..., it follows that an investment that triples in value every three years is best.
• a_n = 3*n+2. a_1 + a_2 + ... + a_1000 = 1000*(5+3002)/2
• a_0 = 21, a_1 = -3, a_2 = 3/7. Sum = 147/8.