27 (A) AND (B)

27. Utility. Utility is a type of function that occurs in economics. When a consumer receives x units of a cer- tain product, a certain amount of pleasure, or utility U, is derived. The following is a graph of a typical utility function. U A 200 g (4,161) a U 95' 150 (3.138) I E (2,109) | E: 100 ' _ ' a: (1. 70) j E I D 50 I 0 1 2 3 4 at Number of units of product a) Find the average rate of change of U as x changes from 0 to 1; from 1 to 2; from 2 to 3; from 3 to 4. \\a b) Why do you think the average rates of change are decreasing as x increases? 30. Compound interest. The amount of money, A(t), in a savings account that pays 6% interest, compounded quar- terly for t years, when an initial investment of $2000 is made, is given by A(t) = 2000 (1.015) 4 a) Find A(3). b) Find A(5). c) Find A(5) - A(3). A(5) - A(3) d) Find , and interpret this result. 5 - 3