In 1975, when the United Nations was formed, there were 51 member nations. In 1987, there were 159 member nations. Write an equation that gives the number of nations in the UN, y, in terms of the year, t. Let t=0 correspond to 1945 and assume that membership followed a linear pattern.
if t = 0 corresponds to 1945
then 1987 --> 42
so think of it as two ordered pairs
(0, 51) and (42, 159)
slope = (159-51)/(42-0) = 108/42 = 18/7
N = (18/7)t + b
but (0,51) would be the y-intercept
N = (18/7) t + 51
Even though we can do the math, the question itself it ridiculous. Membership is not a linear function at all, it would be a "step function".
At present, there are about 200 countries, and according to our equation , that total was reached in about 2003, and the number of countries currently members of the UN would be 223
To find an equation that gives the number of nations in the UN, y, in terms of the year, t, we can use the information provided and assume that membership followed a linear pattern.
We know that in 1975, there were 51 member nations and in 1987, there were 159 member nations. Since we assume a linear pattern, we can find the slope of the line using the formula:
slope (m) = (change in y) / (change in t)
Let's calculate the slope:
change in y = 159 - 51 = 108
change in t = 1987 - 1975 = 12
Now, we can substitute the values into the slope formula:
m = 108 / 12 = 9
The slope of the line is 9, which means that for every year, the number of member nations increased by 9.
Next, to find the y-intercept, we can choose one of the given years as a reference point. Let's use 1975.
Using the slope-intercept form of a linear equation, which is y = mx + b (where m is the slope and b is the y-intercept), we can substitute the values we have:
51 = 9 * 0 + b
Simplifying the equation:
51 = b
Therefore, the y-intercept (b) is 51.
Finally, we can write the equation that represents the number of nations, y, in terms of the year, t:
y = 9t + 51
So, the equation is y = 9t + 51.