Question

Ebbinghaus' Law of Forgetting (Example 4) states that if a task is learned at a performance level P0, then after a time interval t the performance level P satisfies log(P) = log(P0) − c log(t + 1) where c is a constant that depends on the type of task and t is measured in months. Use the Law of Forgetting to estimate a student's score on a biology test two years after he got a score of 84 on a test covering the same material. Assume that c = 0.3 and t is measured in months. (Round your answer to the nearest whole number.) P = __________

Answer 1

Using Ebbinghaus' Law of Forgetting, the estimated test score after two years from an initial score of 84 with a forgetting constant of 0.3 is approximately 32, rounded to the nearest whole number.

Step-by-step explanation:

Ebbinghaus' Law of Forgetting suggests that memory retention decays over time following a mathematical formula. To estimate a student's biology test score after two years, given an initial score of 84 and a constant c equal to 0.3, we apply the formula:

log(P) = log(P0) − c log(t + 1)

First, convert time in years to months: 2 years = 24 months. Then, plug the values into the formula:

log(P) = log(84) - 0.3 log(24 + 1) = log(84) - 0.3 log(25)

Using a calculator for logarithms:

log(P) ≈ 1.9243 - 0.3(1.3979) ≈ 1.9243 - 0.4194 ≈ 1.5049

Now, raise 10 to the power of each side to solve for P:

P = 10^1.5049 ≈ 10^1.5

P ≈ 31.62

The estimated performance level, or test score, after two years, is approximately 32 when rounded to the nearest whole number.