The table gives the annual rates of growth of a country's population for selected years from 1970 projected to 2049. Complete parts (a) through (c). a. Find a logarithmic function that models the rate, y, as a function of the number of years after 1960. Annual Growth Rate 2.01 (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) Year 1970 1980 1.69 b. Find an exponential function that models the rate, y, as a function of the number of years after 1960. 1990 2000 2010 2020 2030 2040 1.52 1.21 (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) c. Graph each model on the same axes with the data. Which of the following correctly graphs the logarithmic function with the data? 1.11 0.93 0.74 0.63 OB. 2049 0.48 OA OC. OD. ........ Which of the following correctly graphs the exponential function with the data? OA OB ...... Oc. OD. Determine which model is the better fit to the data. The model is a better fit compared to the other model.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 29PT: A radiation safety officer is working with 112 grams of a radioactive substance. After 17 days,...
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The table gives the annual rates of growth of a country's population for selected years from 1970 projected to 2049. Complete parts (a) through (c).
a. Find a logarithmic function that models the rate, y, as a function of the number of years after 1960.
Annual
y =|
Year
Growth Rate
(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)
1970
2.01
1980
1.69
b. Find an exponential function that models the rate, y, as a function of the number of years after 1960.
1990
1.52
2000
1.21
y=
2010
1.11
(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)
2020
0.93
c. Graph each model on the same axes with the data. Which of the following correctly graphs the logarithmic function with the data?
2030
0.74
2040
0.63
2049
0.48
А.
В.
С.
OD.
Which of the following correctly graphs the exponential function with the data?
A.
В.
С.
OD.
Determine which model is the better fit to the data.
The
V model is a better fit compared to the other model.
Transcribed Image Text:The table gives the annual rates of growth of a country's population for selected years from 1970 projected to 2049. Complete parts (a) through (c). a. Find a logarithmic function that models the rate, y, as a function of the number of years after 1960. Annual y =| Year Growth Rate (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) 1970 2.01 1980 1.69 b. Find an exponential function that models the rate, y, as a function of the number of years after 1960. 1990 1.52 2000 1.21 y= 2010 1.11 (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) 2020 0.93 c. Graph each model on the same axes with the data. Which of the following correctly graphs the logarithmic function with the data? 2030 0.74 2040 0.63 2049 0.48 А. В. С. OD. Which of the following correctly graphs the exponential function with the data? A. В. С. OD. Determine which model is the better fit to the data. The V model is a better fit compared to the other model.
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