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 1sxs 11. Use this information to complete parts (a) through (c) below. LnReg y = a+b ln x a = 29,67892724 E Click the icon to view the table. b= 29.78535801 W Click the icon to view the scatterplot. a. Explain why a logarithmic function was used to model the data. Choose the correct answer below. O 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. Use the graphing calculator screen to express the model in function notation, with numbers rounded to the nearest whole number. f(x) = 30 + 30 In x (Type an expression using x as the variable.) c. According to the model in part (b), what percentage an adult size brain does a have at age 10? A child has % of an adult size brain at age 10. (Round to the nearest whole number as needed.) Growth of the Human Brain Percentage of Adult Size Brain Age 30% 45% 4 77% 87% 8. 92% 10 95% 11 99% Print Done

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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.
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 1sxs 11. Use this
information to complete parts (a) through (c) below.
LnReg
y = a+bln x
a = 29.67892724
E Click the icon to view the table.
b = 29.78535801
W Click the icon to view the scatterplot.
a. Explain why a logarithmic function was used to model the data. Choose the correct answer below.
O A. The data increase rapidly and then continue to increase even more rapidly.
XB. The data increase at a steady rate.
O C. The data increase rapidly and then begin to decrease.
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 In 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.)
Growth of the Human Brain
Percentage of
Adult Size Brain
Age
1
30%
2
45%
4
77%
6
87%
8
92%
10
95%
11
99%
Print
Done
Transcribed Image Text: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 1sxs 11. Use this information to complete parts (a) through (c) below. LnReg y = a+bln x a = 29.67892724 E Click the icon to view the table. b = 29.78535801 W Click the icon to view the scatterplot. a. Explain why a logarithmic function was used to model the data. Choose the correct answer below. O A. The data increase rapidly and then continue to increase even more rapidly. XB. The data increase at a steady rate. O C. The data increase rapidly and then begin to decrease. 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 In 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.) Growth of the Human Brain Percentage of Adult Size Brain Age 1 30% 2 45% 4 77% 6 87% 8 92% 10 95% 11 99% Print Done
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 1sxs 11. Use this
information to complete parts (a) through (c) below.
LnReg
y = a+b In x
a = 29.67892724
E Click the icon to view the table.
b= 29.78535801
W Click the icon to view the scatterplot.
a. Explain why a logarithmic function was used to model the data. Choose the correct answer below.
O A. The data increase rapidly and then continue to increase even more rapidly.
XB. The data increase at a steady rate.
O c. The data increase rapidly and then begin to decrease.
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 In 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.)
Growth of the Human Brain
100어
60-
40-
20-
0-
10 12
Age
Print
Done
Transcribed Image Text: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 1sxs 11. Use this information to complete parts (a) through (c) below. LnReg y = a+b In x a = 29.67892724 E Click the icon to view the table. b= 29.78535801 W Click the icon to view the scatterplot. a. Explain why a logarithmic function was used to model the data. Choose the correct answer below. O A. The data increase rapidly and then continue to increase even more rapidly. XB. The data increase at a steady rate. O c. The data increase rapidly and then begin to decrease. 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 In 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.) Growth of the Human Brain 100어 60- 40- 20- 0- 10 12 Age Print Done
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