According to the US Bureau of the Census, the world population in the year 1950 was A=2555360972, and in 2000 it was B=6079006982. We'll use A and B so we don't have to keep writing those large and idiosyncratic numbers. We usually use y and x in the equation of a line, but in this and the following problem let's use N and t instead. t stands for time and N for the size of the population.

Question

According to the US Bureau of the Census, the world population in the year 1950 was A=2555360972, and in 2000 it was B=6079006982. We'll use A and B so we don't have to keep writing those large and idiosyncratic numbers. We usually use y and x in the equation of a line, but in this and the following problem let's use N and t instead. t stands for time and N for the size of the population.

If
N(t)=mt+b
such that N(1950)=A and N(2000)=B, then m= and and b= .

Answer 1

I believe you posted this question awhile ago. Anyway, you should get that

N(1975) = 4,317,183,977

How?
Use the equation for linear interpolation:
y = y₀ + (y₁ - y₀) [ (x - x₀)/(x₁ - x₀) ]

Putting it into context...
N(1750) = A + (B - A)[(1975 - 1950)/(2000 - 1950)]

Answer 2

Whoops, in the last line, I meant " N(1975) " and not " N(1750) "

Answer 3

Much Ado About Nothing.

two ordered pairs (1950 , 2555360972) and
(2000 , 6079006982)

slope = (6079006982 - 2555360972)/(2000-1950)
= 70472920.2 ---> m for N(t)= mt+b
using the first point:
2555360972 = 70472920.2(1950) + b
b = -1.348668 x 10^11

so we have N(t) = 70472920.2t -1.348668 x 10^11

checking for 2nd point, if t = 2000
N(2000) = 70472920.2(2000) - 1.348668 x 10^11
= 6079007000 , close enough

Answer 4

To find the values of m and b in the equation N(t) = mt + b given that N(1950) = A and N(2000) = B, we can set up a system of equations.

First, let's substitute the values of t and N into the equation for 1950:
N(1950) = 1950m + b = A

Next, let's substitute the values of t and N into the equation for 2000:
N(2000) = 2000m + b = B

Now we have two equations with two unknowns, m and b. We can solve this system of equations to find their values.

Subtract the first equation from the second equation:
(2000m + b) - (1950m + b) = B - A
50m = B - A

Divide both sides of the equation by 50:
m = (B - A) / 50

To find the value of b, plug this value of m into either of the original equations. Let's use the first equation:
1950m + b = A

Replace m with (B - A) / 50:
1950((B - A) / 50) + b = A

Now, simplify the equation:
39(B - A) + b = A
39B - 39A + b = A

Rearrange the equation to solve for b:
b = A - 39B + 39A
b = 40A - 39B

Therefore, the value of m is (B - A) / 50, and the value of b is 40A - 39B.