The table gives the annual rates of growth of a country's population for selected yearsfrom 1970 projected to 2049. Complete parts (a) through (c).Year197019801990200020102020203020402049AnnualGrowth Rate2.031.671.561.211.150.970.760.640.41hpH a. Find a logarithmic function that models the rate, y, as a function of thenumber of years after 1960.y=(Type an expression using x as the variable. Use integers or decimals for anynumbers in the expression. Round to three decimal places as needed.)b. Find an exponential function that models the rate, y, as a function of thenumber of years after 1960.y=7(Type an expression using x as the variable. Use integers or decimals for anynumbers in the expression. Round to three decimal places as needed.)c. Graph each model on the same axes with the data. Which of the followingcorrectly graphs the logarithmic function with the data?O A.OC.OOB.OD.NNext3:13 PM11/20/2022

Given the table of population growth of a country in selected years from 1970 to 2049. Years after 1960 Annual growth rate 10 2.03 20 1.67 30 1.56 40 1.21 50 1.15 60 0.97 70 0.76 80 0.64 89 0.41 (a) To find a model logarithmic function that models the rate y as a function of the number of years after 1960. (b) To find a model logarithmic function that models the rate y as a function of the number of years after 1960. (a) Use a calculator to find the logarithmic function that models the rate y as a function of the number of years after 1960 using the values given in the table. Switch On the TI-83 calculator and press STAT button, go to EDIT and select 1 and press ENTER. In the column L1, enter the entries of the first column of the table. In the column L2, enter the entries of the second column of the table. Press 2nd and Home to come back to the Home screen. Now choose STAT option again and go to CALC and then scroll down to LnReg and press ENTER. It gives the logarithmic model as y=a+blnx where a=3.809, b=-0.713 i.e. y≃3.809-0.713lnx (b) Use a calculator to find the exponential function that models the rate y as a function of the number of years after 1960 using the values given in the table. Switch On the TI-83 calculator and press STAT button, go to EDIT and select 1 and press ENTER. In the column L1, enter the entries of the first column of the table. In the column L2, enter the entries of the second column of the table. Press 2nd and Home to come back to the Home screen. Now choose STAT option again and go to CALC and then scroll down to ExpReg and press ENTER. It gives the logarithmic model as y=a*b^x where a=2.593, b=0.982 i.e. y≃2.5930.982x (c) The graph of both the functions y≃3.809-0.713lnx, y≃2.5930.982x that models the given data along with the data is as follows. Here the blue curve represents the logarithmic function that models the given data and the orange curve represents the exponential function that models the given data. Thus option B correctly graphs the logarithmic function with the given data.