Answer to Question #198815 in Algebra for Tayyaba

Question

An experiment was conducted to determine the effects of elapsed time on a 

person's memory. Subjects were asked to look at a picture which contained 

many different objects. After studying the pictures, they were asked to recall as 

so many of the objects as they could. At different time intervals following this, 

they would be asked to recall as many objects as they could. Based on the 

experiment, the following function was developed:

 = f(t) = 90 - 30 ln(t) where t ≥ 1

For this function represents the average percent recall as a function of time 

since studying the pictures (measured in hours). A value of = 50 would 

indicate that at the corresponding time t the average recall for the study group 

was 50 percent. 

Answer 1

Given function,

f(t)=90-30ln(t)

At, f(t)=50%=0.5

$0.5=90-30ln(t)\\30ln(t)=9.5\\[9pt]ln(t)=\dfrac{89.5}{30}=2.98\\[9pt]t=19.68\sim 20$