Please help me with this question.Thank you! **Learning Theory Study on Exam Retesting**Students in a learning theory study were given an exam and then retested monthly for 6 months with an equivalent exam. The data obtained in the study are shown in the table, where $ t $ is the time in months after the initial exam and $ s $ is the average score for the students.| $ t $ (months) | 1 | 2 | 3 | 4 | 5 | 6 ||:---------------|:---:|:---:|:---:|:---:|:---:|:---:|| $ s $ (score) | 84.7 | 78.2 | 72.6 | 68.8 | 66.7 | 65.6 |**Tasks:****(a)** Use a graphing utility to find a logarithmic model for the average score $ s $ in terms of the time $ t $. (Round your coefficients to two decimal places.)$ s(t) = $ [Input Field]**(b)** Use a graphing utility to plot the data and graph the model. How well does the model fit the data?- [ ] The model fits the data well.- [ ] The model does not fit the data well.**(c)** Find the rates of change of $ s $ with respect to $ t $ when $ t = 3 $ and $ t = 5 $. (Round your answer to one decimal place.)$ t = 3 $ [Input Field]$ t = 5 $ [Input Field]**(d)** Interpret the meaning of the rates of change found in part (c) in the context of the problem.After 3 months, the average score is decreasing at a rate of [Input Field] points. After 5 months, the average score is decreasing at a rate of [Input Field] points.

Name: Please help me with this question.Thank you! **Learning Theory Study o
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Description: Please help me with this question.Thank you! **Learning Theory Study on Exam Retesting**Students in a learning theory study were given an exam and then retested monthly for 6 months with an equivalent exam. The data obtained in the study are shown in

Since you have posted a question with multiple subparts, we will solve the first three subparts for you. To get the remaining subparts solved please repost the complete question and mention the subparts to be solved. Given, t 1 2 3 4 5 6 s 84.7 78.2 72.6 68.8 66.7 65.6a)Find a logarithmic model for the average score s in terms of t: The general equation of model, s(t)=a+blnt Plug the value (1,84.7) in the general equation we get, 84.7=a+bln(1)84.7=a+b(0)a=84.7 Plug the value (2,78.2) in the general equation we get, 78.2=a+bln(2)78.2=84.7+bln(2)78.2-84.7=b(0.693147)-6.5=0.693147bb=-6.50.693147b=-9.37752b=-9.38 Therefore s(t)=84.7-9.38lntb)Graph the data given in the table, The model sets the data well,c)Find the rate of change of s with respect to t, s(t)=84.7-9.38lnt Differentiate with respect to t we get, s'(t)=0-9.381ts'(t)=-9.38t Put t=3 we get, s'(3)=-9.383=-3.1267s'(3)=-3.1 Put t=5 we get, s'(5)=-9.385=-1.876s'(5)=-1.9

Math

Calculus

Students in a learning theory study were given an exam and then retested monthly for 6 months with an equivalent exam. The data obtained in the study are shown in the cable, where t is the time in months after the initial exam and s is the average score for the students. 1 2 3 4 5 6 t 84.7 78.2 72.6 68.8 66.7 65.6 (a) Use a graphing utility to find a logarithmic model for the average score s in terms of the time t. (Round your coefficients to two decimal places.) s(t) = (b) Use a graphing utility to plot the data and graph the model. How well does the model fit the data? O The model fits the data well. O The model does not fit the data well. (c) Find the rates of change of s with respect to t when t = 3 and t = 5. (Round your answer to one decimal place.) t = 3 t = 5

Students in a learning theory study were given an exam and then retested monthly for 6 months with an equivalent exam. The data obtained in the study are shown in the cable, where t is the time in months after the initial exam and s is the average score for the students. 1 2 3 4 5 6 t 84.7 78.2 72.6 68.8 66.7 65.6 (a) Use a graphing utility to find a logarithmic model for the average score s in terms of the time t. (Round your coefficients to two decimal places.) s(t) = (b) Use a graphing utility to plot the data and graph the model. How well does the model fit the data? O The model fits the data well. O The model does not fit the data well. (c) Find the rates of change of s with respect to t when t = 3 and t = 5. (Round your answer to one decimal place.) t = 3 t = 5

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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Please help me with this question.

Thank you!

**Learning Theory Study on Exam Retesting**

Students in a learning theory study were given an exam and then retested monthly for 6 months with an equivalent exam. The data obtained in the study are shown in the table, where $ t $ is the time in months after the initial exam and $ s $ is the average score for the students.

| $ t $ (months) | 1 | 2 | 3 | 4 | 5 | 6 |
|:---------------|:---:|:---:|:---:|:---:|:---:|:---:|
| $ s $ (score) | 84.7 | 78.2 | 72.6 | 68.8 | 66.7 | 65.6 |

**Tasks:**

**(a)** Use a graphing utility to find a logarithmic model for the average score $ s $ in terms of the time $ t $. (Round your coefficients to two decimal places.)

$ s(t) = $ [Input Field]

**(b)** Use a graphing utility to plot the data and graph the model. How well does the model fit the data?

- [ ] The model fits the data well.
- [ ] The model does not fit the data well.

**(c)** Find the rates of change of $ s $ with respect to $ t $ when $ t = 3 $ and $ t = 5 $. (Round your answer to one decimal place.)

$ t = 3 $ [Input Field]

$ t = 5 $ [Input Field]

**(d)** Interpret the meaning of the rates of change found in part (c) in the context of the problem.

After 3 months, the average score is decreasing at a rate of [Input Field] points. After 5 months, the average score is decreasing at a rate of [Input Field] points.

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