## Paul F.'s Resources Assuming the same growth rate = 2.5% per year f(x) = Population f(x) = 6 (1.025)^x  12 = 6 (1.025)^x 2 = (1.025)^x Log 2 = Log (1.025)^x Log 2 = x Log (1.025)   Power Rule for Logarithms x = Log 2 / Log (1.025) = 0.3010 / .0107 = 28.1 ... x + y = - 116 x -  y =  - 52 Add the equations to eliminate y 2x = - 168 x = - 84 Plug back in to x + y = - 116 so y = -32   Check  -84 - (-32) = - 52   checks ok ! There is a rational zero test. All rational solutions to f(x) = 0 will be contained in the set of ± r / ± s where r = the factors of the coefficient xn = the highest power term s = the factors of the coefficient of x0 = the constant term   For f (x)= 2x^3-4x^2+5x-3 ... x - y = 10  and x + 2y/3 = 16 Subtract  - 5y/3 = - 6 y = 18/5  => x = 16 - 2/3 (18/5)  = 204/15 ==>So x , y = 54/15 , 204/15  <==   Check   (204 - 54)/15 = 150/15 = 10 the population of purple martins p  the population of raccoons, r p(r)= 750 - 3.75r the mosquito population m m (p) = 50,000 -45p.   So if r = 0  then p(0) = 750 m(p) = m(750) = 50,000 - 45 (750) m = 16,250 Invoke Conservation of Energy ..... Change in PE + Change in KE = 0  .... dPE = dKE     d=delta or change 1. The half of the chain off the table falls a distance L/2. It's change in potential energy dPE is rho (L/2) g (L/2)     Note;  [PE = mgh; rho L =... Rates are \$85 and \$120            Rate   x    Time   =   \$ charged  1st     r               15             15 r  2nd  205 - r    ... Ages now 15 and 43   E + F = 58 2 (E+13) = F+13 2E + 26 = F + 13 2E - F = - 13   E + F = 58 Adding these equations eliminates F 3E = 45 E = 15 thus if E+F=58 then F=43 Checking 43+13=56 15+13=28  checks... \$4500 at 3%   &  \$7500 at 8%   Total interest = \$735 Let N(3) = Amt after 1 yr of the 3% investment of P Let N(8) = Amt after 1 yr of the 8% investment of P + \$3000   N(3) + N(8) = P + (P+3000) + 735 = 2P + 3735   N(3)... A model is a replica of something original or real For example, architects build out of cardboard, small models of a proposed building. An equation, differential, integral, quadratic or even just linear, models the natural world in some respect. For example again  y = x2 models... My method is nearly identical to Arturo O. Suvat formula   v2 - u2  =  2  a  s v = final velocity   u = initial velocity   s = distance This assumes constant acceleration/deceleration So .... 0 - u2  = 2  a  s        The... Go to www.khanacademy.com You can learn any one of 100 subjects with their videos, including Math, Physics, Biology, Chemistry, etc. Its just like having your own private tutor. If you need more help, message me here at WyzAnt.com Good luck ! So the data are 6 14 15 22 23 23 28 34 Mode is 23 Median 22.5 Mean 165 / 8 = 20.625