Pick ONE of the problems from this collection "Advanced Functions Questions" that has not already been solved. Pretend that you are tutoring someone who has never seen these problems before and give a detailed demonstration of its solution.

15) Solve: (43 )X + 1 = 25x x + 2 16) Solve: eX _ 3 : [i] 86 17) The growth in the mouse population at a certain county dump can be modeled by the exponential function A(t)= 906e0'012t, where t is the number of months since the population was first recorded. Estimate the population after 36 months. 18) The decay of 938 mg of an isotope is given by A(t)= 938e'0'022t, where t is time in years since the initial amount of 938 mg was present. Find the amount (to the nearest milligram) left after 96 years. 19) The sales of a mature product (one which has passed its peak) will -at decline according to the function S(t) : Soe , Where t is time in years since the peak sales. Find the sales of a product 17 years after its peak sales if a = 0.22 and SO : 77,500. 20) The number of reports of a certain Virus has increased exponentially since year 0. The number of cases can be approximated using the function r(t) : 119 0.008t Estimate the number of cases in year 40. , where t is the number of years since year 0. 0.048t 21) An element decays at the rate of S(t) : se , where s is the initial amount in grams and t is the time in years since this initial amount was present. If you have a 7l-gram piece of this element, how many grams will you have 5 years from now? Round your answer to the nearest tenth of a gram. 22) Solve: log5 125 = x 23) Solve: log3 % = x 24) Solve: log7 1712 = x 25) Solve: logX 625 = 4 [d 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) Advanced Functions 1) Solve: 2) Solve: 3} Solve: 4) Solve: 5} Solve: 6) Solve: 7) Solve: 8) Solve: 9) Solve: 10) Solve: 11) Solve: 12) Solve: 13) Solve: 14) Solve: 4096X = 8 X [l] = 729 9 HX _ 2401 256 4-X = 256 1) 2) 3} 4) 5} 6) 7) 3) 9) 10) 11) 12) 13) 14) 26) 26) Solve: X = 810g8 13 27 ) 27) Solve: x = log10 0.01 28 ) 28) Solve: x = 1082 V8 29) 29) Solve: logx 9 = - 2 30) 30) Solve: log4 X = 3 31) 31) Solve: 10g5 X = -3 32) 32) Solve: log(x - 5) 10 =1 33) 33) Solve: log(x + 7) 11 = 1 34) 34) Solve: 8x - 32 = logx 1 35) 35) Suppose f(x) = logax and f(4) = 2. Find f(16). 36) 36) Suppose f(x) = logax and f(4) = 2. Find f 1 37) 37) Suppose f(x) = loga(x) and f(7) = 2. Find f(343). 38) 38) Suppose f(x) = loga(x) and f(5) = 2. Find f 15 39) 39) Evaluate: 100 08107 40) 40) Evaluate: log10(0.01)9 41) 41) Evaluate: 1000 081010 42) 42) Evaluate: log10(0.0001) 10 w