Question

19&20

The population P (in thousands) of Reno, Nevada from 2000 through 2007 can be modeled by P = 346.8e" where / represents the year, with 1 0 corresponding to 2000. In 2005, the population of Reno was about 395,000. According to the model, during what year will the population reach 486,000.00 O a 2009 Ob.2005 O c.2021 Od 2013 Oe.2017 QUESTION 20 Use the Remainder Theorem and synthetic division to find the function value. Verify your answers using another method. h(x)=x-22 - 5x+6, h(-8)

Answer 1

Colution Given P=346.8ekt P=395,000 t = 5, K=? 395,000 = 3468 e Sk psk - 395000 346.8 = 1138.945006 take In both sides :- In esk = In 1935. 98.5006 5k In = 7.037892799 5k = 7.03789 2999 K = 7.037892799 K= 1.40757856 OY K = 1- 4077 P = 486.000 K=1.407% = ? 486.000 = 346 Re: 4076 1.4076_ 486000 346.8

e 12074 = 1401.384083 take In both sides in e 14078 = In 1901.384083 1.4077 In = 7.24-5215658 1.404 = 7.245215658 t = 7.245215658 1.40 ut= 5. 175154041 Year's from 2000+ 5 =(2005) In 2005 population will be 486,000 Hence, ③ we can say's that option js 2005 is right angwer. t=5.175154041 OR A a 5 years

hem = x²2x²5x+6 h (-8) put akt-8) in the h (8) = (-8) 22 (8) ² - 5(-8) +6. = -512-128 + 4046 =-690 +46 h (8) = -594 Synthatic Division -8 L1 -2 -8 Ti -10 -5 6 80 -600 75 -5941 Remainder (x² - 10x +75) Ents)[03-222-56kt6 » 3401 +75 Long divison on²-58 -1601²-pore 75% 76 Hence we can 7.5x+600 stay that hes) (-594) Remainder is not a factor of h(x)=x²22²-5x16