The number of years n required for an investment at interest rate r to double in value must satisfy (1 + r)n = 2. Using ln 2 = .69 and the approximation ln(1 + r) ≈ r valid for small r, show that n ≈ 69/i, where i is the interest rate percentage (that is, i = 100r). Using the better approximation ln(1+r) ≈ r − 1 2 r2, show that for r ≈ .08 there holds n ≈ 72/i.

Marvin wrote a check of $58.25 for the water bill and $450 for rent. he also made a deposit of $124.16. how much is his new balance after writing the checks and making the deposit?

At a student café, there are equal numbers of two types of customers with the following values. the café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., she cannot price-discriminate). students with early classes students without early classes coffee 70 60 banana 51 101 the marginal cost of coffee is 10 and the marginal cost of a banana is 40. the café owner is considering three pricing strategies: 1. mixed bundling: price bundle of coffee and a banana for 161, or just a coffee for 70. 2. price separately: offer coffee at 60, price a banana at 101. 3. bundle only: coffee and a banana for 121. do not offer goods separately. assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle. for simplicity, assume there is just one student with an early class, and one student without an early class. price strategy revenue from pricing strategy cost from pricing strategy profit from pricing strategy 1. mixed bundling $ $ $ 2. price separately $ $ $ 3. bundle only $ $ $ pricing strategy yields the highest profit for the café owner.

12.     to produce a textured purée, you would use a/an a. food processor. b. wide-mesh sieve. c. immersion blender d. food mill. student a   incorrect which is correct answer?