College Algebra

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. e 2X -8e*+7=0 The solution set expressed in terms of logarithms is {} 2 Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. log 3 (x + 21) - log 3 (X - 5) = 3 3 The function P(x) = 95 - 25 log 2x models the percentage, P(x), of students who could recall the important features of a classroom lecture as a function of time, where x represents the number of days that have elapsed since the lecture was given. The figure shows the graph of the function. After how many days do only a quarter of the students recall the $38 8 important features of the classroom lecture? (Let P(x) = 25 and solve for x.) Locate the point on the graph that conveys Percent this information 40- 20- 3 4 6 8 10 1214 Days 4 The exponential models describe the population of Country B A= 1173.1 e 0.007t the indicated country, A, in millions, t years after 2010. Which countries have a decreasing Country C A= 35.5 e 0.019t population? By what percentage is the population Country D A= 123.3 e - 0.005t of these countries decreasing each year? Country E A= 141.9 e - 0.0021 5 The exponential model A = 381.1 + 0.006t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of he country will be 407 million. The half-life of the radioactive element unobtanium-43 is 20 seconds. If 176 grams of unobtanium-43 are initially present, how many grams are present after 20 seconds? 40 seconds? 60 seconds? 80 seconds? 100 seconds? 7 Rewrite the following equation in terms of base . Express the answer in terms of a natural logarithm, then round to three decimal places. y = 2.9(0.9)&quot