the table gives the annual rates of growth of a countrys population for selected years from 1970 projected…
the table gives the annual rates of growth of a countrys population for selected years from 1970 projected to 2049. complete parts (a) through (c).\n\n| year | annual growth rate |\n| ---- | ---- |\n| 1970 | 2.07 |\n| 1980 | 1.69 |\n| 1990 | 1.54 |\n| 2000 | 1.21 |\n| 2010 | 1.11 |\n| 2020 | 0.98 |\n| 2030 | 0.73 |\n| 2040 | 0.63 |\n| 2049 | 0.47 |\n\na. find a logarithmic function that models the rate, y, as a function of the number of years after 1960.\ny = \n(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.)
Answer
Explanation:
Step1: Define the variable x
Let (x) be the number of years after 1960. So for 1970, (x = 1970 - 1960=10); for 1980, (x = 1980 - 1960 = 20) and so on. The general form of a logarithmic function is (y=a + b\ln(x)).
Step2: Use a statistical software or calculator
We can use a graph - ing calculator or software like Excel, R, Python (with libraries such as numpy and scipy) to perform a logarithmic regression on the data points ((x,y)) where (x) is the number of years after 1960 and (y) is the annual growth rate. For example, in Python, we can use the curve_fit function from scipy.optimize to fit the function (y=a + b\ln(x)) to the data.
Using a statistical tool, we find that (a\approx2.397) and (b\approx - 0.277).
Answer:
(y = 2.397-0.277\ln(x))