Without further study, you forget things as time passes. A model of human memory gives the percentage, p, of acquired knowledge that a person retains after t weeks. The formula is p = (100 – a)e-bt + a, where a and b vary from one person to another. If a = 18 and b = 0.6 for a certain student, how much information will the student retain two weeks after learning it?
54% or 43%? I keep ending up with 26%
(100-18)e^-.6(2) +18
24.69792538+18
= 42.6
So round up. 43%
To determine the percentage of information retained by the student two weeks after learning it, we can use the given formula: p = (100 – a)e^(-bt) + a.
Substituting the given values a = 18 and b = 0.6 into the formula, we have:
p = (100 – 18)e^(-0.6 * 2) + 18
Simplifying this expression further:
p = 82 * e^(-1.2) + 18
Calculating e^(-1.2) approximately:
e^(-1.2) ≈ 0.301
Substituting this value back into the equation:
p = 82 * 0.301 + 18
Calculating this expression:
p ≈ 24.682 + 18
p ≈ 42.682
Therefore, the student will retain approximately 42.682% of the information two weeks after learning it.
To calculate the percentage of information the student will retain two weeks after learning it, we need to substitute the given values for a and b into the formula and solve for p.
Given:
a = 18
b = 0.6
t = 2 weeks
The formula for retention of knowledge is:
p = (100 - a)e^(-bt) + a
Substituting in the values:
p = (100 - 18)e^(-0.6 * 2) + 18
Using a calculator, calculate the exponential term first, then continue solving:
p = 82e^(-1.2) + 18
Now, we can calculate the value of p:
p ≈ 82 * 0.301194 + 18
p ≈ 24.7073488 + 18
p ≈ 42.7073488
Therefore, the student will retain approximately 42.71% of the information two weeks after learning it.