In 1995, the life expectancy of males in a certain country was 73.8 years. In 2001, it was 76.5 years. Let E represent the life expectancy in year t and let t represent the number of years since 1995. The linear function E(t) that fits the data is__. Use the function to predict the life expectancy of males in 2005 E(10)=
let 1995 correspond with t=0
then you have two ordered pairs
(0,73.8) and (6,76.5)
now find the slope and proceed as if you were finding the equation of a line in the form
y = mx + b or
E(t) = mt + b
drwls had answered the almost identical question here
http://www.jiskha.com/display.cgi?id=1282186087
To find the linear function that fits the given data, we need to determine the equation of a straight line in the form y = mx + b, where y represents the life expectancy (E), x represents the number of years since 1995 (t), m represents the slope of the line, and b represents the y-intercept.
First, we need to determine the slope (m) of the line. The slope of a line can be found using the formula:
m = change in y / change in x
In this case, the change in y is the difference in life expectancy (E) between the years 2001 and 1995 (76.5 - 73.8), and the change in x is the difference in years since 1995 (2001 - 1995).
Therefore, the slope (m) can be calculated as:
m = (76.5 - 73.8) / (2001 - 1995) = 2.7 / 6 = 0.45
Next, we need to determine the y-intercept (b) of the line. The y-intercept is the value of y when x is 0 (representing the year 1995). Since we are given that the life expectancy in 1995 was 73.8, the y-intercept (b) is 73.8.
Hence, the equation of the linear function E(t) that fits the data is:
E(t) = 0.45t + 73.8
To predict the life expectancy of males in 2005 (t = 10), we substitute t = 10 into the equation:
E(10) = 0.45(10) + 73.8
E(10) = 4.5 + 73.8
E(10) = 78.3
Therefore, the predicted life expectancy of males in 2005 is 78.3 years.