11. d'w Find - - for the given function. W = 6z Z d'w dz2 12. A company's total cost, in millions of dollars, is given by C(t) =70 - 50e * where t is the time in years since the start-up date. 150- The graph of C(t) is shown to the right. Find each of the following. a) The marginal cost, C'(1) a bj c'To) c) C'(5) 75- d) Find lim C(t) and lim C'(t). t-+ 0o 1-+00 30 a) C'(t) = (Do not include the $ symbol in your answer.) b) C'(0) = $ million per year (Simplify your answer. Do not include the $ symbol in your answer.) c) C'(5) = $ per year (Simplify your answer. Round to the nearest thousand as needed. Do not include the $ symbol in your answer.) d) lim C(t) = $ million 1-+0 (Simplify your answer. Do not include the $ symbol in your answer.) lim C'(t) = $ per year 1+00 (Simplify your answer. Do not include the $ symbol in your answer.) 13. A restaurant purchased kitchen equipment on January 1, 2017. On January 1, 2019, the value of the equipment was $14,450. The value after that date was modeled as follows. V(t) = 14,450 e - D.1621 ) What is the rate of change in the value of the equipment on January 1, 2019? b) What was the original value of the equipment on January 1, 2017? a) The rate of change in the value of the equipment on January 1, 2019 was dollars per year. Type an integer or decimal rounded to two decimal places as needed.) b) The original value of the equipment on January 1, 2017 was $ Type an integer or decimal rounded to two decimal places as needed.)14. Suppose that you are given the task of learning 100% of a block of knowledge. Human nature is such that we retain only a percentage P of knowledge t weeks after we have learned it. The Ebbinghaus learning model asserts that P is given by P(t) = Q+ (100 - Q)e -ki, where Q is the percentage that we would never forget and k is a constant that depends on the knowledge learned. Suppose that Q = 50 and k = 0.7. Complete parts (a) through (e) below. a) Find the percentage retained after 0 weeks, 1 week, 2 weeks, 6 weeks, and 10 weeks. Complete the table to the right. Time Passed Percentage 0 weeks 1 week 2 weeks 6 weeks 10 weeks [Round to one decimal place as needed.) b) Find lim P(t). t-+00 lim P(t) = % (Simplify your answer.) 1+00 c) Sketch a graph of P. Choose the correct graph below. O A O B. O c. O D. 100- 100- AF 100- d) Find the rate of change of P with respect to time t. P(t)= e) Interpret the meaning of the derivative. Choose the correct answer below. O A. The derivative is the rate at which exactly 10% of knowledge is lost. O B. The derivative is the amount of time it takes to lose all knowledge that can be forgotten. O C. The derivative represents the amount of knowledge retained forever. O D. The derivative is the rate at which the retained knowledge changes per week
