Question

Sweden's population increased almost linearly from 3.5 million in 1850 to 7.0 million in 1950. Calculate when Sweden's population was 4.0 million according to this model.

y=kx+m
7 = 100k + 3.5
3.5 = 100k
3.5/100 = k
0.035 = k

So the formula is y = 0.035x+3.5

And I assume the solution is 0.035*4+3.5 which is 3.64

Would this be correct? I know it looks like I'm just looking for confirmation but I'm trying to also do the question before hand, even if it can be wrong, just to give it a go.

Answer 1

First of all, you did not define what the x and y in your equation represent.
If y is the population in millions and x is the year, then you had two ordered pairs:
(1850,3.5) and (1950,7)
slope = (7-3.5)/(1950-1850) = 3.5/100 = 7/200

so y = (7/200)x + b
sub in (1950,7)
7 = (7/200)(1950) + b
b = -61.25

y = (7/200)x - 61.25
so when is y = 4 ?

4 = (7/200)x - 61.25
65.25 = 7/200 x
x = 1864.38.. So it happened in appr 1864

another quick way:
1850 -- 3.5
x ------- 4
1950 --- 7

now set up a simple interpolation ratio:
(x-1850)/(1950-1850) = (4-3.5)/(7-3.5)
(x - 1850)/100 = 0.5 / 3.5 = 1/7
7x - 7(1850) = 100
7x = 13050
x = 1864.28.. same as above

Answer 2

I completely screwed this one, Thanks for the reply!