A group of students retake the written portion of a driver? s test after several months without reviewing the material. A model used by psychologists describes retention of the material by the function a = 90 - 10 log (t + 2), where a is the average score at the time t (in weeks). Use the model to predict the number weeks when the average score is 75.

Question

Dale Watts

Mathematics

21 June, 00:52

A group of students retake the written portion of a driver? s test after several months without reviewing the material. A model used by psychologists describes retention of the material by the function a = 90 - 10 log (t + 2), where a is the average score at the time t (in weeks). Use the model to predict the number weeks when the average score is 75.

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India Jones · Answer 1

1. Given a (t) = 90 - 10 log (t + 2) = 75 or

10*log (t + 2) = 90-75 = 15 or log (t+2) = 1.5 or

(t+2) = 10^ (1.5) or t = - 2+[10*√10] = 29.622 or 29.6 weeks. hence the option, "a. 29.6 weeks" is correct.