Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. |n(a) - |n(b) = |n(a b) for all positive real numbers a and b. 0 True. Take a = 4 and b = 2. Then |n(a) |n(b) = |n(4) |n(2) = |n(g) = |n(2). And |n(a b) = |n(4 2) = |n(2). 0 True. This is one of the Laws of Logarithms. 0 False. |n(a b) = |n(a) - |n(b) only for negative real numbers a and b. 0 False. |n(a b) = |n(a) |n(b) only for positive real numbers a > b. False. Take a = 2 and b = 1. Then |n(a) |n(b) = |n(2) |n(1) = |n(2) 0 = |n(2). But |n(a b) = |n(2 1) = |n(1) = 0. Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus says: 0 Integration and Differentiation are inverse processes up to additive constants 0 All of the statements are true 0 The integral of the derivative of a real function is the function itself The derivative of the integral of a real function is the function itself 0 Integration and Differentiation complement each other in Calculus 0 None of the statements are true Interest. Suppose the manager of a bank provides a new formula to calculate interest for merging two loans together: Suppose there are two loans with one interest rate at 4% and a second loan at 5% . The manager writes the rst part of the formula for the new interest rate as e(4ln(5) + 5|n(4)) Which of the following is equivalent to the manager's expression? () 6640000 (3 87399 0 320000 640000 0 625+81024 () 6320000 0 1649 O 0 Find the values of x for which the function is continuous. X f( x) = 7x-+ 3 O all x, x # - V W O all x, X # V/ w 3 O all x, X # 3 O all x, x * - all real numbers\fA cell phone company estimates that t months after releasing a new model of their phones, the total number of units sold (in millions) will be given by Mr) = 10(1 e'o'St)3 where 0 S t S 12. (a) About how many units will be sold 2 months after the release of the new model? O 5.1 thousand O 26.3 thousand O 5.1 billion None of the other options 0 26.3 billion (b) How fast will the new model be selling 2 months after its release? 0 1.6 million/month O 4.4 million/month O 12.0 million/month 2.2 million/month O 6.0 million/month