T 1971 1982 1992. 2003
P. 4. 5. 6. 7
Find slope of each line segment connecting consecutive data points from the table
M1=
M2=
M3=
Does the polynomial 0.09t-175 give a good estimate for the world population in year t?
To find the slope of each line segment connecting consecutive data points from the table, we can use the formula for slope:
Slope (m) = (y2 - y1) / (x2 - x1)
Let's calculate the slopes:
For the first line segment connecting (1971, 4) and (1982, 5):
m1 = (5 - 4) / (1982 - 1971) = 1 / 11 = 1/11
For the second line segment connecting (1982, 5) and (1992, 6):
m2 = (6 - 5) / (1992 - 1982) = 1 / 10 = 1/10
For the third line segment connecting (1992, 6) and (2003, 7):
m3 = (7 - 6) / (2003 - 1992) = 1 / 11 = 1/11
Therefore,
M1 = 1/11
M2 = 1/10
M3 = 1/11
Now, let's analyze the polynomial 0.09t - 175 to determine if it gives a good estimate for the world population in year t.
The given polynomial equation represents a linear relationship between t (years) and the estimated world population. The coefficient 0.09 represents the average increase in the world population per year, and the constant term -175 represents an initial estimate for the world population.
To determine if it gives a good estimate, we need to compare the estimated values from the polynomial equation to the actual population values from the table.
Let's plug in the values of t from the table and compare the estimated population values to the actual population values:
For t = 1971:
Estimated population = 0.09 * 1971 - 175 = 177.39 - 175 = 2.39
Actual population = 4
For t = 1982:
Estimated population = 0.09 * 1982 - 175 = 178.38 - 175 = 3.38
Actual population = 5
For t = 1992:
Estimated population = 0.09 * 1992 - 175 = 179.28 - 175 = 4.28
Actual population = 6
For t = 2003:
Estimated population = 0.09 * 2003 - 175 = 180.27 - 175 = 5.27
Actual population = 7
By comparing the estimated population values to the actual population values, we can see that the polynomial 0.09t - 175 does not provide a good estimate for the world population in the given years since the estimated values are significantly different from the actual values.