MATH lll 82013 PracticeTest3a(Ch.4,5)SHOW ALL WORKNO CREDIT WILL BE GIVEN FOR THE ANSWERS WITHOUT WORK4 points each1. Write each equation in its equivalent exponential form (do not solve for x)a) log(a + 4):2b)ln(x-l):62. Write each equation in its equivalent logarithmic form (do not solve for x)a) 12*:3xb) d*s:253. Expand the logarithmic expression completely and simplift:Je4)\ Y'l4. Combine the logarithmic expression to a single logarithm0.5(log5x + logsy) - 2 log5(x + 1)5. The firnction y :2.557e0'0t6h describes the world population, in billions, x years after1949.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 billionpeople?6. The growtlr model P : 104.9 (1.016S)t describes Mexico's population t years after20Q3. 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 rateof 0.4% per year. Find the exponential model to describe the population of Russia x yearsafter 2005.8. Solve each equation for x, round to 2 decimals:a) 7"*2: 410b) log5(4x + 1) + log5x - I9. The formula A : 18.9 e 0 00s5t models the population of New-York State, in millions, tyears after 2000. According to this model, when will the population of New-York Statedouble in size?10. Find f(g(x)) and g(f(x)) for f(x) :4x- 3 and g(x): 5x2 -2f(e(x)):e(f(x)):11. Find the inverse f-'(*) if f (x):t"[912. Use trans_formations to sketch the graph of f(x) : - 1og2(x - 3)7 points13.. The regular price of a cell phone is x dollars. Let f(x) : x - 145 and g(x) :0.8xa) Describe what the functions f(x) and g(x) model in terms of the price of the cell phone.f(x) isg(x) isb) Find f(g(x)) and g(f(x)), describe what do they represent in terms of the price of thecell phone.f(e(x)):and it representse((x)):and it representsc) Which of them models the greater discount on the cell phone?.14.Fory-- (x-3)2-4a) Find the direction the parabola opensb) find x- and y-coordinates of the vertexc) find y-interceptd) graph the function15. Write the equation ofthe quadratic function whose vertex is at (2, 12) and whosegraph passes through the point (4, 0).16. The function f(x) : - 0.064x2 + 0.99x + 2.2 represents the number of US farms, inmillions, 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)sriow ALL woRKTestldCh.4,5)NO CREDIT WILL BE GIVEN FOR THE ANSWERS WITHOUT WORK4 points each1. write each equation in its equivalent exponential form (do not solve for x)a) log(a + 4):2 oA+Ll= lO", A+q =l0Ob)ln(x-l):66X-l = e-2. write each equation in its equivalent logarithmic form (do not solve for x)a) 12*:3x@t,^csx) = xb) sv* s:25fuAs+u=73. Expand the logarithmic expression completely and simplifu:'"[#) = h pe')- 9"" Us = .0,t+ (*"'- ;hy=-4-3 +2-ft-?4. Combine the logarithmic expression to a single logarithm0.5(log5x + logsy) - 2 log5(x + 1)0,,;ry;o;i"'.Loa" (^*)'= ,fu+F,- /v, ('rl" '5. rhe tunction y :2.557e0 0r6ex describes ,^" -rrrk{^("r,ff!rl"ons, x years after1949.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 billionPeoPle? I o = r, fs 7 eo'o /[7 'x(^ /& -l = co/6f x'' ' (A 'ssz )X r80,J l('/q+80'7 =floAf'7i n 2130-=--6. The growth model P : 104.9 (1.016S)t describes Mexico's population t years after2003. Rewrite the model in terms of the base e. (Round to 4 decimals)P= lo,.(,Q eo,cl5/t7. The population of Russia was 144.5 million in 2005 decreasing with a continuous rateof 0.4% per year. Find the exponential model to describe the population of Russia x yearsafter 2005.p = l,/l,f e- o'oorx-8. Solve each equation for x, round to 2 decitnals:a) 7"*2: 410(r ^ )Pn7 . h,tl rox = fujleU47- A ;- l,c1b) log5(4x + 1) + log5x: 1bqf P/y r/)x = I<J (x +r)y = u4XLrX-f=odouble in size?t, = Q9'0055Lt = 4?== = t)f,, o30,005f10. Find f(g(x)) and g(f(x)) for f(x) :4x-3 and g(x): sxz -2f(e(x)) --4 bl^-t)- se(f(x)):s^(t/x-s)\2:xW11. Find the inverse .f '^(*) if f (x)= t"l?,,l rtl=e, ry y:;='An?-/ tft +ss_ -/ tq-x='T= T=,-\(Y-=r') x+-[l')/ lt' 'l/^ -5)/9. The formula A: 18.9 e 0'00sst models the population of New-York State, in millions, tyears after 2000. According to this model, when will the population of New-York State(n z/2€=&!+4vy-b ^3 /: 3+2.(x-T: e/ (l -= J *A, 111. Use transformations to sketch the graph of f(x) : - log2(x - 3)t Z l1ItIt,i7 points13. The regular price of a cell phone is x dollars. Let f(x) : x - 145 and g(x) : 0.8xa) Describe what the functions f(x) and g(x) model in terms of the price of the cell phone.f(x) isCA o'l- A n /.,AnZ Alq f /z'sca",-*g(x)is W'u 4 a f ak't le/e /-ric-a"-,-Ab) Find f(g(x)) and g(f(x)), describe what do they represent in terms of the price of thecell phone.r(e(x)): O,8 X - lq fand it represents {h oru A re ob.cz dL artd a'*',-a //(fes(f(x)):6\r\^'', n8(x-!4Q = o'8-(.--/ /4and it npnnit' 4,f/"2_ _a $ /+f &i€o/^a/ W' aff&e/ , il.p /-/cnwa| a/& h'or,-/+ 2?d/.tcrd by 2o7oc) Which of them models the greater discount on the cell phone?f t2fU1 ginz/ ,gw-eft4 d'sc'u-/hJrr r) ,-" | -+t'X ^( x-t)14.Fory=-(x -12- 4a) Find the direction the parabola opensb) find x- and y-coordinates of the vertexc) find y-intercept - 1- t4 = gd) graph the function= -l 10 de,.vnX:3t A = -Ll-z-f-6-8-ro-tL'15. Write the equation of the quadratic flrnction whose vertex is at (2, 12) and whose'tlXgraph passes through the point (4, 0).t = o (y-rl_7rtlo = Q (+-l)-+tL-t2 " t'!qQ :'3y=4.-30-z) +tL:= 7,7 /acalrl a74+t /$osl 77 Turs .16. The function f(x) = - 0.064x2 + 0.99x + 2.2 represents the number of US farms, inmillions, where x is the number of decades after 1850.a) In which year did the number of US farms reach a maximum?f,=*2 (-o.o61)l85D +77 ? /u7 -':'b) What was the maximum number of farms? Round to the nearest tenth of a million.f (l tl = -o,Mt/'7'7L+0'?{'7'7 +z'z = 6'0,W,;,*-ts-;^ n27