Question

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.

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. 

Answer 2

Answer: There are 29 weeks approximately when the average score is 75.

Step-by-step explanation:

Since we have given that

$a=90-10\log (t+2)$

Here, a is the average score.

and t denotes the number of weeks.

Since we have given that the average score is 75.

so, we put a = 75 in the above equation.

$75=90-10\log (t+2)\\\\75-90=-10\log (t+2)\\\\-15=-10\log (t+2)\\\\\frac{15}{10}=\log (t+2)\\\\1.5=\log (t+2)\\\\\text{Taking 10 to the power on both sides}\\\\10^{1.5}=t+2\\\\31.6=t+2\\\\t=31.6-2\\\\t=29.62\ weeks\\\\t\approx 29\ weeks$

Hence, there are 29 weeks approximately when the average score is 75.