Difficulty Understanding This Need Help Please

Question

In a learning experiment involving memory, subjects were given a certain amount of time to study the objects laid out on a table. Later, they were asked to recall as many items as they could. The proportion of items recalled was estimated to be linearly related to the effective study time (in seconds). For an effective study time of 5 seconds, the proportion of items recalled was 0.31. When given 8 seconds, the proportion of items recalled was 0.40.



1. Determine the function that estimates proportion of items recalled based on study time.
2. What proportion of items was recalled with 10 seconds of effective study time?

Answer 1

As it's given that the relationship between study time and items recalled, the equation will be in the slope-intercept form: y = mx + b

Let's say that study time runs on the x-axis and items recalled is on the y-axis.

Slope = rise/run = (y₂ - y₁)/(x₂ - x₁) (0.40 - 0.31)/(8 - 5) = 0.09/3 = 0.03 (m)

Use one of pairs to determine (b)

0.31 = 0.03(5) + b → 0.31 = 0.15 + b

b = 0.16

y = 0.03x + 0.16

For 10 sec y = 0.03(10) + 0.16 = 0.3 + 0.16 = 0.46 items

Take this function with a little skepticism. For 0 seconds, they'd remember 0.16 of the items!!