In 1992, the life expectancy of males in a certain country was 71.4 years. In 1996 it was 73.6 years.
Let E represent the life expectancy in year t and let t represent the number of years in 1992.
E(t)=____t+____
Use the function to predict the life expectancy of males in 2005.
E(13)=___
To find the equation for life expectancy, we need to find the slope and the y-intercept using the given information.
Let's assign t = 0 for the year 1992. In 1992, the life expectancy was 71.4 years, so we have the point (0, 71.4).
Let's also assign t = 4 for the year 1996. In 1996, the life expectancy was 73.6 years, so we have the point (4, 73.6).
Now, we can find the slope using the formula:
slope = (change in y)/(change in x) = (73.6 - 71.4)/(4 - 0) = 2.2/4 = 0.55
Using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the known values to find the equation for the life expectancy:
71.4 = 0.55(0) + b
b = 71.4
So, the equation for the life expectancy is:
E(t) = 0.55t + 71.4
To predict the life expectancy in 2005 (t = 13), we can substitute t = 13 into the equation:
E(13) = 0.55(13) + 71.4
E(13) = 7.15 + 71.4
E(13) = 78.55
Therefore, the predicted life expectancy of males in 2005 is approximately 78.55 years.
To find the equation that represents the life expectancy of males in the given country, we can use the information provided in 1992 and 1996.
In 1992, the life expectancy of males was 71.4 years. Since we want to use the number of years in 1992 (t) as a variable, we can represent this as t=0.
In 1996, the life expectancy increased to 73.6 years, which would be represented by t=4 (as it is 4 years after 1992).
Now we can calculate the slope of the line using the formula:
slope (m) = (change in y) / (change in x)
change in y = 73.6 - 71.4 = 2.2
change in x = 4 - 0 = 4
slope (m) = 2.2 / 4 = 0.55
Now we have the slope (m), we can find the equation using the point-slope form of a line:
y - y1 = m(x - x1)
Since t=0 and E=71.4 is our first point, we plug these values into the equation:
E - 71.4 = 0.55(t - 0)
Simplifying this equation, we get:
E - 71.4 = 0.55t
Now we can rewrite the equation in the form E(t) = ___t + ___:
E(t) = 0.55t + 71.4
To predict the life expectancy of males in 2005, we substitute t=13 into the equation:
E(13) = 0.55(13) + 71.4
Calculating this equation, we get:
E(13) = 7.15 + 71.4
Simplifying, we find:
E(13) = 78.55
Therefore, the predicted life expectancy for males in the given country in 2005 is 78.55 years.