Human Memory Test
Math help: work problem with log; please help :]?
Human Memory Model : Students participating in a psychological experiment attended several lectures. After the last lecture, and every month for a year after that, the students were tested to see how much of the material they remembered. The average score for the group are given by the memory model:
f(t) = 90 – 15 log (base 10) (t+1) , (0) is less than or equal to (t) is less than or equal to (12)
where t is the time in the month.
a) Use the average graph utility to graph the function over the specific domain
b) What is the average score on the exam (t = 0)?
c) What is the average score after 6 months?
d) What is the average score after 12 months?
e) When would have the average score decrease to 75?
Basically you are given the formula that just happens to have a log in it and you are asked in part (a) to draw the graph on your graphing calculator. You would enter the equation just like it looks, but since the calculator uses x instead of t you would use x. Also be sure to use base 10 logs which is shown just as “log” on the calculator, not base e logs which is shown as “ln”. You would use x (t) window from 0 to 12 on the calculator and the highest y value you would need to look at would be about 100 so set the y window from 0 to 100.
(b) To find the average score when t = 0 just put 0 in for t in the formula. So..
f(0) = 90 – 15log(0+1) = 90 So when the time was 0 mo (at the start) the score was 90.
(c) Do the same for 6 months
f(6) = 90 -15log(6+1) = 90 -15log(7) = 77.32
d) Same for 12 mo.
f(12) = 90 – 15log(12+1) = 90 – 15log(13) = 73.29
(e) To find when the test score is 75, put in 75 for f(t) and solve for t….
75 = 90 – 15log(t+1)
15log(t+1) = 90 – 75
15log(t+1) = 15
log(t+1)=1 dividing both sides by 15
t+1 = 10^1 changing from log form to exponential form
t = 9 months
Good luck….
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