Am not good with story prombles could someone please help. Can you show me how to come up with answer so that I understand it.
The bith rate in the United states in 1996 was 14.7 births per thousand population. In 2006, the birth rate was 14.14 births per thousand.
A.Write two order pairs of the form (year after 1996, bith rate per thousand population)
Think the order pair is (1996,14.7),(2006,14.14)
B. Assume that the relationship between years after 1996 and bith rate per thousand is linear over this period. Use the order pairs from part (a) to write an equation of the line rating years to birth rate.
C. Use the linear equation from part(b) to estimate the birth rate in United States in year 2016
A) correct
B) slope = (14.14-14.7)/(2006-1996) = -.56/10
= -.056
y = -.056t + b, where t is the year
use 1st pair (1996,14.7)
14.7 = -.056(1996) + b
b = 126.476
y = -.056t + 126.476
C) plug in t = 2016 to get y
Sure, I can help you with that!
A. To write two ordered pairs of the form (year after 1996, birth rate per thousand population), we can use the given information. We have the birth rate in 1996 as 14.7 births per thousand population and in 2006 as 14.14 births per thousand population. Therefore, the two ordered pairs would be: (0, 14.7) and (10, 14.14). The first number in each ordered pair represents the number of years after 1996, and the second number represents the birth rate per thousand population.
B. To find the equation of the line relating years after 1996 to birth rate, we can use the formula for the equation of a line: y = mx + b. Here, 'y' represents the birth rate, 'm' represents the slope of the line, 'x' represents the number of years after 1996, and 'b' represents the y-intercept.
First, we need to find the slope 'm'. The formula for finding the slope is: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two ordered pairs. Using the ordered pairs we found in part A: (0, 14.7) and (10, 14.14), we can substitute the values into the slope formula:
m = (14.14 - 14.7) / (10 - 0)
m = (-0.56) / 10
m = -0.056
Now we have the slope 'm'. To find the y-intercept 'b', we can use one of the ordered pairs and substitute the values into the equation y = mx + b. Let's use the first ordered pair (0, 14.7):
14.7 = (-0.056)(0) + b
14.7 = b
So, the y-intercept 'b' is 14.7.
Now we can write the equation of the line relating years after 1996 to birth rate:
y = -0.056x + 14.7
C. To estimate the birth rate in the United States in the year 2016 using the linear equation we found in part B, we need to substitute the value of 'x' as 20 (since 2016 is 20 years after 1996) into the equation:
y = -0.056(20) + 14.7
y ≈ -1.12 + 14.7
y ≈ 13.58
Therefore, the estimated birth rate in the United States in the year 2016 is approximately 13.58 births per thousand population.