d) Find the rate of change of P with respect to time t.P'(t) =el Interpret the meaning of the derivative. Choose the correct answer below? A. The derivative is the amount of time it takes to lose all knowledge that can be forgotte? B. The derivative is the rate at which exactly 10% of knowledge is lost.c The derivative is the rate at which the retained knowledge changes per weekD. The derivative represents the amount of knowledge retained forever.

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 ", where Q is the percentage that we would never forget and k is a constant that depends on the knowledge learned. Suppose that Q = 35 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 o 6 weeks % 10 weeks (Round to one decimal place as needed.) b) Find lim P(t). lim P(t) = % (Simplify your answer.) 1 -+ 00 c) Sketch a graph of P. Choose the correct graph below. O B. O D. O A. O C. AP AP AP AP O 100- 100- 100- 100- Submit quiz