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natima [27]
3 years ago
12

Students in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t​

months, the average score​ S(t), as a​ percentage, was found to be given by the following​ equation, whereStudents in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t​ months, the average score​ S(t), as a​ percentage, was found to be given by the following​ equation, where t>=0.
Required:
a. What was the average score when they initially took the test, t=0?
b. What was the average score after 4 months?
c. What was the average score after 24 months?
d. What percentage of their original answers did the students retain after 2 years?
e. The maximum of the function is_____%.

Mathematics
1 answer:
juin [17]3 years ago
6 0

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.}

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.

 

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Answer:

See explanation and attachment

Step-by-step explanation:

SOH CAH TOA is a mnemonic.

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RS=2x-8, ST = 11, RT = x+10
ziro4ka [17]

Answer:

Equation~=~\Large\boxed{2x+3=x+10}

x~=~\Large\boxed{7}

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Step-by-step explanation:

<u>Given information</u>

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<u>Derived expression from the given information</u>

<em>Presumably, I think this is a combination of segments</em>

RS+ST=RT

<u>Substitute values into the given expression</u>

(2x-8)+(11)=(x+10)

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\Large\boxed{2x+3=x+10}

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<u>Subtract x on both sides</u>

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\Large\boxed{x=7}

<u>Substitute the x value into corresponding expressions to determine the final value</u>

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