Part c: What percentage of an adult size brain does a child have at age 10?Part d: Determine whether the value from the model is larger or smaller than the value in the table. **Data Analysis of Human Brain Growth from Ages 1 to 11**The following data demonstrate that the human brain does not grow linearly or steadily between the ages of 1 and 11. Below is a table showing this information, accompanied by a scatter plot.### Scatter Plot Explanation:The scatter plot displays the percentage of an adult brain, \( y \), for a child at age \( x \), where \( 1 \leq x \leq 11 \). Use this information to complete the questions provided. The linear regression equation shown is:\[ y = a + b \ln x \]where \( a = 29.67892724 \) and \( b = 29.78535801 \).**Tasks:****a. Determine Why a Logarithmic Function is Used:**- Choose the best explanation: - **A.** The data increase rapidly and then continue to increase even more rapidly. - **B.** The data increase at a steady rate. - **C.** The data increase rapidly and then begin to decrease. - **D.** The data increase rapidly and then begin to level off.**b. Express the Model in Function Notation:**- Use the graphing calculator to express the model, rounding numbers to the nearest whole number: \[ f(x) = 30 + 30 \ln x \] (Type an expression using \( x \) as the variable.)**c. Calculate the Percentage at Age 10:**- Using the model from part (b), calculate what percentage of an adult-size brain a child has at age 10. Round to the nearest whole number.**Growth of the Human Brain Data Table:**| Age | Percentage of Adult Size Brain ||-----|-------------------------------|| 1 | 30% || 2 | 45% || 4 | 77% || 6 | 87% || 8 | 92% || 10 | 95% || 11 | 99% |This information provides insights into the growth pattern of the human brain during early development, emphasizing significant growth within this age range. The data in the following table indicate that between the ages of 1 and 11, the human brain does not grow linearly or steadily. A scatter plot for the data is shown below the table.The graphing calculator screen to the right displays the percentage of an adult brain, \( y \), for a child at age \( x \), where \( 1 \leq x \leq 11 \). Use this information to complete parts (a) through (c) below.- Click the icon to view the table.- Click the icon to view the scatterplot.**a. Explain why a logarithmic function was used to model the data. Choose the correct answer below.**- A. The data increase rapidly and then continue to increase even more rapidly.- B. The data increase at a steady rate.- C. The data increase rapidly and then begin to decrease.- D. The data increase rapidly and then begin to level off.**Correct Answer**: D. The data increase rapidly and then begin to level off.**b. Use the graphing calculator screen to express the model in function notation, with numbers rounded to the nearest whole number.**\( f(x) = 30 + 30 \ln x \)(Type an expression using x as the variable.)**c. According to the model in part (b), what percentage of an adult size brain does a child have at age 10?**A child has ____% of an adult size brain at age 10. (Round to the nearest whole number as needed.)**Graph Explanation: Growth of the Human Brain**The scatter plot shows the growth of the human brain as a percentage of the adult size, plotted against the age in years. The x-axis represents the age (from 0 to 12 years), and the y-axis represents the percentage of adult brain size (from 0 to 100%). The points plotted suggest rapid growth during early years that start to level off as age increases.

Name: Part c: What percentage of an adult size brain does a child have at ag
Uploaded: 2024-03-05T11:52:21.000Z
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Description: Part c: What percentage of an adult size brain does a child have at age 10?Part d: Determine whether the value from the model is larger or smaller than the value in the table. **Data Analysis of Human Brain Growth from Ages 1 to 11**The following dat