MATH lll 82013 PracticeTest3a Ch 4 5 SHOW ALL WORK NO CREDIT WILL BE GIVEN FOR THE ANSWERS WITHOUT WORK 4 points each 1 Write each equation in its equivalent exponential form do not solve for x a log a 4 2 b ln x l 6 2 Write each equation in its equivalent logarithmic form do not solve for x a 12 3x b d s 25 3 Expand the logarithmic expression completely and simplift Je4 Y l 4 Combine the logarithmic expression to a single logarithm 0 5 log5x logsy 2 log5 x 1 5 The firnction y 2 557e0 0t6h describes the world population in billions x years after 1949 a What is the world s population continuous growth rateinYo b According to this model in which year will the world s population reach l0 billion people 6 The growtlr model P 104 9 1 016S t describes Mexico s population t years after 20Q3 Rewrite the model in terms of the base e Round to 4 decimals 7 T e population of Russia was 144 5 million in 2005 decreasing with a continuous rate of 0 4 per year Find the exponential model to describe the population of Russia x years after 2005 8 Solve each equation for x round to 2 decimals 7 2 410 a b log5 4x 1 log5x I 00s5t 9 The formula A 18 9 e 0 models the population of New York State in millions t years after 2000 According to this model when will the population of New York State double in size 10 Find f g x and g f x for f x 4x f e x e f x 11 Find the inverse f if f x t 9 3 and g x 5x2 2 12 Use trans formations to sketch the graph of f x 1og2 x 3 7 points 13 The regular price of a cell phone is x dollars Let f x x 145 and g x 0 8x a Describe what the functions f x and g x model in terms of the price of the cell phone f x is g x is b Find f g x and g f x describe what do they represent in terms of the price of the cell phone f e x and it represents e x and it represents c Which of them models the greater discount on the cell phone 14 Fory x 3 2 4 a Find the direction the parabola opens b find x and y coordinates of the vertex c find y intercept d graph the function 15 Write the equation ofthe quadratic function whose vertex is at 2 12 and whose graph passes through the point 4 0 16 The function f x 0 064x2 0 99x 2 2 represents the number of US farms in millions where x is the number of decades after 1850 a In which year did the number of US farms reach a maximum b What was the maximum number of farms Round to the nearest tenth of a million MATH 111 F 70t2 TestldCh 4 5 sriow ALL woRK NO CREDIT WILL BE GIVEN FOR THE ANSWERS WITHOUT WORK 4 points each 1 write each equation in its equivalent exponential form do not solve for x a log a 4 2 o A Ll lO A q l0O b ln x l 6 X l e 6 2 write each equation in its equivalent logarithmic form do not solve for x a 12 3x t csx b sv x s 25 fuAs 7 u 0 t 3 Expand the logarithmic expression completely and simplifu h pe 9 Us 4 3 2 ft 4 Combine the logarithmic expression to a single logarithm 0 5 log5x logsy 2 log5 x 1 0 ry o i Loa 5 rhe tunction y 2 557e0 0r6ex describes fu F hy v rl rrrk r ff rl ons x years after 1949 a What is the world s population continuous growth rate ino o l 6q b According to this model in which year will tlie world s population r u h 10 billion PeoPle 7 o r fs 7 eo o x l co 6f x A ssz l q 80 7 floAf 7 r80 J X I i n 2130 6 The growth model P 104 9 1 016S t describes Mexico s population t years after 2003 Rewrite the model in terms of the base e Round to 4 decimals P lo Q eo cl5 t 7 The population of Russia was 144 5 million in 2005 decreasing with a continuous rate of 0 4 per year Find the exponential model to describe the population of Russia x years after 2005 p l l f e o oorx 8 Solve each equation for x round to 2 decitnals a 7 2 410 Pn7 h tl ro A l c1 x fujle U47 r b log5 4x 1 log5x ss tq 5 tft x T T Y r x lt l l 1 bqf r x I P y J x r y u 4XLrX f o 9 The formula A 18 9 e 0 00sst models the population of New York State in millions t years after 2000 According to this model when will the population of New York State double in size n z 2 t Q9 0055L t 0 005f 4 t f o3 10 Find f g x and g f x for f x f e x 4 bl t s 4x 3 and g x sxz 2 4 e f x s t x s 2 xW 11 Find the inverse l e f ry y b e 3 T if f x t l l rt y An v 3 2 x J A 1 l 11 Use transformations to sketch the graph of f x log2 x 3 hJrr t r x t t X Z l1 It I t i 7 points 13 The regular price of a cell phone is x dollars Let a Describe what the functions f x is g x is CA o l x 145 and g x 0 8x f x and g x model in terms of the price of the cell phone A n AnZ A W u 4 a f f x lq f z sca ak t le e ric a A b Find f g x and g f x describe what do they represent in terms of the price of the cell phone r e x O 8 X lq and it represents s f x 6 r e h f oru A re ob cz d L artd a o 8 4 and it npnnit 4 f 2 a f i o a W wa n8 x 4Q a h or 2 d tcrd by 2o7o a f aff e il p cn c Which of them models the greater discount on the cell phone d sc u f t2fU1 ginz gw eft4 14 Fory x 12 4 l 10 de vn X 3t A Ll a Find the direction the parabola opens b …