The town of appleville recorded the following dates and populations.
YEAR POPULATION
1985 51.5
1985 53
1990 56
1995 62
Estimate the approximate population of Appleville in 1988 by finding an equation and then substituting.
HELP!!!
Do this exactly the way w and I did the previous one
Omg! Would you just please help me I have 3 kids and I'm cooking dinner, please just help me understand this one!
It says approximate so put it on the straight line between 1985 and 1990
what is that line?
m = (56-53)/(1990-1985) = 3/5
so y = (3/5)x + b
when x = 1985, y = 53 so
53 = (3/5) (1985) + b
53 = 1191+b
b = -1138
so
y = (3/5) x - 1138 between 1985 and 1990 approximately
y at 1988 = (3/5)(1988) - 1138
= 1192.8-1138 = 54.8 approximately
Now before dinner is ready go back and understand the one w did and I explained.
We can find this equation using different methods (Least square method, Lagrange interpolation polynomial method, ...)
Which you are applying?
What is did here is called "linear interpolation" and I suspect it is what your text wants looking at the level of your previous problem. We could get more sophisticated fitting these four points with a cubic polynomial but based on the other problem I am quite sure your class is not there yet. I am quite sure by approximate they mean fit with a straight line between the closest points, linear interpolation.
Yes Mgraph, but look at the previous question further down. I think this class is on straight lines. I could be wrong of course.
I can not see them solving for a least square fit or using Lagrange polynomials.
To estimate the approximate population of Appleville in 1988, we can use linear interpolation.
First, let's plot the given data points on a graph, with the years on the x-axis and the population on the y-axis.
1985 51.5
1985 53
1990 56
1995 62
The points (1985, 51.5) and (1985, 53) have the same x-value, so we can consider them as a single data point.
Next, we need to find the equation of the line that passes through these data points. We can use the slope-intercept form of a linear equation, y = mx + b, where y represents the population, x represents the year, m represents the slope, and b represents the y-intercept.
To find the slope (m), we can use the formula:
m = (change in y) / (change in x).
Using the points (1985, 51.5) and (1990, 56), the change in y is 56 - 51.5 = 4.5, and the change in x is 1990 - 1985 = 5. Therefore, the slope is m = 4.5 / 5 = 0.9.
Since we have two points (1985, 51.5) and (1990, 56), we can substitute one of the points into the equation y = mx + b to solve for b.
Using the point (1985, 51.5):
51.5 = 0.9 * 1985 + b
51.5 = 1786.5 + b
b = 51.5 - 1786.5
b = -1735
Now we have the equation:
y = 0.9x - 1735
To estimate the population in 1988, we substitute x = 1988 into the equation:
y = 0.9 * 1988 - 1735
y ā 50.92
Therefore, the approximate population of Appleville in 1988 is estimated to be around 50.92.
Note: Linear interpolation assumes that the data points follow a linear trend, which may not always be accurate.