In 1992, the life expectancy of males in a certain country was 73.5 years. In 1996, it was 75.7 years. Let E representthe life expectancy in yeart and let t represent number of years since 1992.
Fill in the linear function E(t) that fits the data
E(t)=____t+____
uses this to prdict the life expectancy of males in 2009
E(17)=____
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To find the slope would it then be 75.7-73.5/73.5
so the slope would be 33.4? or would it just be 2.2?
no
treat you data as two ordered pairs
(0,73.5) and (4,75.7)
then slope =(75.7-73.5)/(4-0) = .55
so your equation is
E(t) = .55t + b
using (0,73.5)
73.5 = 0 + b
b = 73.5
so E(t) = .55t + 73.5
for for E(17) = .55(17) + 73.5 = 82.85
To find the linear function E(t) that fits the data, we need to determine the slope and the y-intercept.
First, let's calculate the slope using the formula: slope = (change in y)/(change in x)
(change in y) = 75.7 - 73.5 = 2.2
(change in x) = 1996 - 1992 = 4
slope = 2.2/4 = 0.55
So, the slope of the linear function E(t) is 0.55.
Now, to find the y-intercept, we can substitute the values of one of the given points (1992, 73.5) into the equation: E(t) = slope * t + y-intercept
73.5 = 0.55 * 0 + y-intercept
y-intercept = 73.5
Therefore, the linear function E(t) is E(t) = 0.55t + 73.5.
To predict the life expectancy of males in 2009, we substitute t = 17 into the equation:
E(17) = 0.55 * 17 + 73.5
E(17) = 9.35 + 73.5
E(17) = 82.85
So, the predicted life expectancy of males in 2009 is 82.85 years.