Answer:
a. 73; b. 48.9; c. 2; d. 33.8; e. 73
Step-by-step explanation:
Assume the function was
S(t)= 73 - 15 ln(t + 1), t ≥ 0
a. Average score at t = 0
S(0) = 73 - 15 ln(0 + 1) = 73 - 15 ln(1) = 73 - 15(0) =73 - 0 = 73
b. Average score at t = 4
S(4) = 73 - 15 ln(4 + 1) = 73 - 15 ln(5) = 73 - 15(1.61) =73 - 24.14 = 48.9
c. Average score at t =24
S(24) = 73 - 15 ln(24 + 1) = 73 - 15 ln(25) = 73 - 15(3.22) =73 - 48.28 = 24.7
d. Percent of answers retained
At t = 0. the students retained 73 % of the answers.
At t = 24, they retained 24.7 % of the answers.
![\text{Percent retention} = \dfrac{\text{24.7}}{\text{73}} \times 100 \, \% = \text{33.8 \%}\\\\\text{The students retained $\large \boxed{\mathbf{33.8 \, \%}}$ of their original knowledge after two years.}](https://tex.z-dn.net/?f=%5Ctext%7BPercent%20retention%7D%20%3D%20%5Cdfrac%7B%5Ctext%7B24.7%7D%7D%7B%5Ctext%7B73%7D%7D%20%5Ctimes%20100%20%5C%2C%20%5C%25%20%3D%20%5Ctext%7B33.8%20%5C%25%7D%5C%5C%5C%5C%5Ctext%7BThe%20students%20retained%20%24%5Clarge%20%5Cboxed%7B%5Cmathbf%7B33.8%20%5C%2C%20%5C%25%7D%7D%24%20of%20their%20original%20knowledge%20after%20two%20years.%7D)
e. Maximum of the function
The maximum of the function is at t= 0.
Max = 73 %
The graph below shows your knowledge decay curve. Knowledge decays rapidly at first but slows as time goes on.