Solve each logarithmic equation. Be sure to reject any values of x that are not in...

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Solve each logarithmic equation. Be sure to reject any values of x that are not in the domain of the original logarithmic expressions. Give the exact answer. Then, when necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 76) log2(x-3) + log x log (x + 2) = 2 82) 3 log x = log 125 108) Complete the table for an investment subjected to n compounding yearly, A = nt P(1+). Round answers to the nearest one decimal place. Amount Invested Number of Compounding Periods Annual Rate Accumulated Amount Time t in years $30,000 12 6.5% $45,000 ? Section 3.5 Exercise Set: Page 507-510, Problems # 30, 36, 37, 40, 48, 58 Use the exponential decay model, A = Apekt to solve the following exercise. Round your final answer to the nearest one decimal place 30) The half-life of aspirin in the bloodstream is 12 hours. How long will it take for the aspirin to decay to 70% of its original dosage? In 2 Use the formula t that gives the time for the population with a growth k rate of k to double to solve the following. Round your final answer to the nearest whole year. 36) The growth model A = 129.0e 0.0106t describes Mexico's population, A, in millions, t years after 2020. a) What is Mexico's growth rate? b) How long will it take for Mexico to double its population? Use the logistic growth model given to solve the following: 37) The following logistic growth function, f(t), describes the number of people, f(t), who have become ill with influenza t weeks after its initial outbreak in a particular community. 100,000 f(t) 1 + 5000e-t a) How many people became ill with the flu when the epidemic began? b) How many people were ill by the end of the fourth week? c) What is the limiting size of the population that becomes ill? 40) The logistic growth model for the world population, f(x), in billions, x years after 1949 is 10.95 f(x) = 1+ 3.51e-0.029x When did the world population reach 7 billion? Use Newton's Law of Cooling T = C + (To + C)ekt, to solve the following exercise: 48) A pizza removed from the oven has a temperature of 450F. It is left sitting in a room that has a temperature of 70F. After 5 minutes, the temperature of the pizza is 300F. a) Use Newton's Law of Cooling to find a model for the temperature of the pizza, after t minutes. b) What is the temperature of the pizza after 20 minutes? c) When will the temperature of the pizza be 140F? 58) Rewrite the following exponential equation in terms of base e. Express the answer in terms of natural logarithms. Then, express the answer with the logarithm rounded to three decimal places. y = 1000(7.3)* 8 Solve each logarithmic equation. Be sure to reject any values of x that are not in the domain of the original logarithmic expressions. Give the exact answer. Then, when necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 76) log2(x-3) + log x log (x + 2) = 2 82) 3 log x = log 125 108) Complete the table for an investment subjected to n compounding yearly, A = nt P(1+). Round answers to the nearest one decimal place. Amount Invested Number of Compounding Periods Annual Rate Accumulated Amount Time t in years $30,000 12 6.5% $45,000 ? Section 3.5 Exercise Set: Page 507-510, Problems # 30, 36, 37, 40, 48, 58 Use the exponential decay model, A = Apekt to solve the following exercise. Round your final answer to the nearest one decimal place 30) The half-life of aspirin in the bloodstream is 12 hours. How long will it take for the aspirin to decay to 70% of its original dosage? In 2 Use the formula t that gives the time for the population with a growth k rate of k to double to solve the following. Round your final answer to the nearest whole year. 36) The growth model A = 129.0e 0.0106t describes Mexico's population, A, in millions, t years after 2020. a) What is Mexico's growth rate? b) How long will it take for Mexico to double its population? Use the logistic growth model given to solve the following: 37) The following logistic growth function, f(t), describes the number of people, f(t), who have become ill with influenza t weeks after its initial outbreak in a particular community. 100,000 f(t) 1 + 5000e-t a) How many people became ill with the flu when the epidemic began? b) How many people were ill by the end of the fourth week? c) What is the limiting size of the population that becomes ill? 40) The logistic growth model for the world population, f(x), in billions, x years after 1949 is 10.95 f(x) = 1+ 3.51e-0.029x When did the world population reach 7 billion? Use Newton's Law of Cooling T = C + (To + C)ekt, to solve the following exercise: 48) A pizza removed from the oven has a temperature of 450F. It is left sitting in a room that has a temperature of 70F. After 5 minutes, the temperature of the pizza is 300F. a) Use Newton's Law of Cooling to find a model for the temperature of the pizza, after t minutes. b) What is the temperature of the pizza after 20 minutes? c) When will the temperature of the pizza be 140F? 58) Rewrite the following exponential equation in terms of base e. Express the answer in terms of natural logarithms. Then, express the answer with the logarithm rounded to three decimal places. y = 1000(7.3)* 8