Word Problem

Question

In 1940, there were 249,767 immigrants admitted to a country. In 2002, the number was 1,014,550.
A. Assuming that the change in immigration is linear, write an equation expressing the number of immigrants, y, in terms of t, the number of years after 1900.
B. Use your result in part A to predict the number of immigrants admitted to the country in 2017.
C. Considering the value of the y-intercept in your answer to A, discuss the validity of using this equation to the model number of immigrants throughout the entire 20th century.

Answer 1

Using a base of 1900, we have two points:

(40, 249767) and (102, 1014550)

 

Slope is change in y over change in x. So that is 764783/62 or about 12335.2

 

Y = mx + b and using the first point we have: 249767 = 12335.2 * 40  + b. Solving we get b = 39756359 (rounding)

 

Now to use it to get the 2017 number. 

 

y = 12335.2(117) + 39756359 or y  =  41199578

 

Clearly the y-intercept is large, so it would need to be checked with the historical record. It is likely too big, which means this method of prediction is not that great.