in 1991 the life expectancy of males in certain county was 68.6 years in 1996 it was 70.9 years let t represent the life expectancy in year t and let t represent the number of years since 1991
I know that model
life expectance= slope*time + constant is the math model here.
first thing, slope:
slope= changelifeexpatance/changetime
= (70.9-68.6)/(1996-1991)=2.3/5
life expectance= 2.3/5 * year + constant
now to find the constant:
life expectancey= 2.3/5 *t + constant where t= (year-1991)
70.9=2.3/5* 5 + constant
solving for constant,
70.9=2.3 + constant
constant= 70.9-2.3=68.6
amazing, so now you have
lifeexpectancey=2.3/5 * t+68.6 where t is the years since 1991
thank u
To find the linear equation that represents the life expectancy over time, we can use the given data points.
Let's assign the year 1991 as t=0. This means that t represents the number of years since 1991.
According to the data, in 1991 (t=0), the life expectancy of males was 68.6 years. This gives us the first data point (t, life expectancy): (0, 68.6).
Similarly, in 1996 (t=5), the life expectancy increased to 70.9 years. This gives us another data point: (5, 70.9).
To find the equation of the line that represents this linear relationship, we can use the formula for a straight line: y = mx + b, where y represents the life expectancy (dependent variable), x represents the number of years since 1991 (independent variable), m represents the slope of the line, and b represents the y-intercept.
Let's calculate the slope (m) using the two given data points:
m = (y2 - y1) / (x2 - x1)
= (70.9 - 68.6) / (5 - 0)
= 2.3 / 5
= 0.46
Now that we have the slope (m), we can substitute it along with one of the data points into the equation to find the y-intercept (b). Let's use the first data point (0, 68.6):
68.6 = (0.46)(0) + b
b = 68.6
Therefore, the equation that represents the life expectancy (t) in years since 1991 is:
life expectancy (t) = 0.46t + 68.6