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.
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
I completely screwed this one, Thanks for the reply!
Yes, you are correct in your approach.
Based on the given model, y = 0.035x + 3.5 represents the relationship between the population (y) and the year (x).
To find when Sweden's population was 4.0 million, you can substitute y = 4.0 into the equation and solve for x:
4.0 = 0.035x + 3.5
0.035x = 4.0 - 3.5
0.035x = 0.5
x = 0.5 / 0.035
x ≈ 14.29
So, according to this model, Sweden's population was approximately 4.0 million around the year 14.29.
Your approach is correct, but there is a minor mistake in your calculation. Let's go through the steps again to find the correct answer.
The given information is that Sweden's population increased almost linearly from 3.5 million in 1850 to 7.0 million in 1950. This can be represented by a linear equation of the form y = kx + m, where y represents the population, x represents the year, k represents the slope, and m represents the initial population in the year 1850.
We can substitute the given values to find the values of k and m:
7.0 = 100k + 3.5 (since 1950 - 1850 = 100 years)
3.5 = 100k
Simplifying the second equation, we have:
k = 3.5/100
k = 0.035
Now we can use the calculated values of k and m to get the population when the year, x, is 4.0 million:
y = 0.035x + 3.5
y = 0.035 * 4 + 3.5
y = 0.14 + 3.5
y = 3.64
So, the correct answer is that according to this model, Sweden's population was 4.0 million around the year 1850+3.64, which is approximately the year 1853.64.
Therefore, the correct answer is 1853.64 (approximately).