In 1950 the life expectancy of women was 72 years. In 1970 it was 75 years. E represents the life expectancy and T the number of years since 1950 (t=0 gives 1950 and t=10 gives 1960).
a. fit a linear equation to predict life expectancy (0,72) AND (20,75)
The answer i got was E=3/20t=72
b. use the function to predict the life expectancy of women in 2003 and 2018.
I don't understand how i am supposed to set this and predict it.
I think you mistyped your equation.
E(t) = 72 + 3/20 t
See, when t=0, E = 72
When t=20, E = 72 + 3/20 (20) = 72 + 3 = 75.
So, now figure E(2003-1950) = E(53)
and E(2019-1950) = E(69)
whats the answer?
Well, predicting the future is always a bit tricky, but let's give it a try with some clownish humor!
a. To fit a linear equation, we need to find the slope (m) and the y-intercept (b). We can use the formula: E = mt + b, where E represents life expectancy and t represents the number of years since 1950.
Using the points (0, 72) and (20, 75), we can calculate the slope:
m = (75 - 72) / (20 - 0) = 3/20
To find the y-intercept, we can substitute one of the points into the equation:
72 = (3/20) * 0 + b
72 = b
So, the linear equation to predict life expectancy would be E = (3/20)t + 72.
b. Now, let's use this equation to predict the life expectancy of women in 2003 and 2018.
For 2003 (t = 53), we substitute t = 53 into the equation:
E = (3/20) * 53 + 72
E = 7.95 + 72
E = 79.95 (or let's round it up to 80)
For 2018 (t = 68), we substitute t = 68 into the equation:
E = (3/20) * 68 + 72
E = 10.2 + 72
E = 82.2 (or we can round it to 82)
So, according to our clownish calculations, the predicted life expectancy for women in 2003 is 80 years and in 2018 is 82 years. But remember, these predictions are just for fun and not scientifically accurate!
To fit a linear equation, we can use the formula for a linear equation in slope-intercept form: y = mx + b, where y is the dependent variable (life expectancy), x is the independent variable (years since 1950), m is the slope, and b is the y-intercept.
a. Fit a linear equation using the given data points (0,72) and (20,75):
Step 1: Calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
= (75 - 72) / (20 - 0)
= 3 / 20
Step 2: Substitute one of the points (0,72) and the calculated slope (m) into the equation y = mx + b, and solve for the y-intercept (b):
72 = (3 / 20) * 0 + b
72 = b
Therefore, the linear equation to predict life expectancy is:
E = (3 / 20)T + 72
b. Use the function to predict life expectancy in 2003 and 2018:
For 2003 (T = 2003 - 1950 = 53):
E = (3 / 20) * 53 + 72
E ≈ 80.25 (rounded to two decimal places)
For 2018 (T = 2018 - 1950 = 68):
E = (3 / 20) * 68 + 72
E ≈ 83.1 (rounded to one decimal place)
Therefore, the predicted life expectancy of women in 2003 would be approximately 80.25 years, and in 2018, it would be around 83.1 years.
To fit a linear equation to predict life expectancy, we can use the formula for a straight line, which is given by the equation y = mx + b, where 'y' represents the dependent variable (in this case, life expectancy), 'x' represents the independent variable (in this case, the number of years since 1950), 'm' represents the slope of the line, and 'b' represents the y-intercept.
a. First, we need to find the slope of the line. We can use the formula for the slope:
m = (y2 - y1) / (x2 - x1)
Given two points (0, 72) and (20, 75), we can substitute the values into the formula:
m = (75 - 72) / (20 - 0) = 3 / 20
So the slope of the line is 3/20.
b. Next, we need to find the y-intercept. We can use one of the given points and the slope to calculate the y-intercept using the formula:
b = y - mx
Using the first given point (0, 72):
b = 72 - (3/20) * 0 = 72
So the y-intercept is 72.
Now we have the equation for the linear function to predict life expectancy:
E = (3/20)T + 72
To predict the life expectancy in 2003, we need to calculate the number of years since 1950. In 2003, T = 2003 - 1950 = 53. Substitute this value into the equation:
E = (3/20) * 53 + 72 = 7.95 + 72 = 79.95
Therefore, the predicted life expectancy for women in 2003 is approximately 79.95 years.
Similarly, to predict the life expectancy in 2018, we calculate the number of years since 1950: In 2018, T = 2018 - 1950 = 68. Substitute this value into the equation:
E = (3/20) * 68 + 72 = 10.2 + 72 = 82.2
Therefore, the predicted life expectancy for women in 2018 is approximately 82.2 years.