Question No. 4:

Part A:

The first census of United States took place in 1790 under Secretary of State Thomas Jefferson; including that there have been total 23 federal censuses till date and the 24^th United States Census is currently in progress with its reference date as April 1, 2020. The following table represents the total population count of last 6 completed censuses of USA;

Year	1960	1970	1980	1990	2000	2010
Population	179,323,175	203,302,031	226,545,805	248,709,873	281,421,906	308,745,538

Table 1

Interpolate all the aforementioned data values by using Lagranges Interpolation method in order to approximate the population of United States of America in 1987.

Part B:

Ohms law states that the voltage drop V across an ideal resistor is linearly proportional to the current I flowing through the resister as in V = IR, where R is the resistance. However, real resistors may not always obey Ohms law. Suppose that you performed some very precise experiments to measure the voltage drop and corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohms law:

I	-1.5	-0.5	-0.25	0.25	0.5	1.5
V	-982	-166.6	-54	54	166.6	982

Table 2

To quantify this relationship, a curve must be fit to the data. Because of measurement error, regression would typically be the preferred method of curve fitting for analysing such experimental data. However, the smoothness of the relationship, as well as the precision of the experimental methods, suggests that interpolation might be appropriate. By using all the set of values given in table 2, apply Newton Divided Difference method to fit the data and compute V at I = - 0.75.