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.