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?
To find the linear function that fits the data, we can use the slope-intercept form of a linear equation: E(t) = mt + b, where m represents the slope and b represents the y-intercept.
To find the slope, we can use the formula:
slope = (change in y) / (change in x)
Given that the life expectancy in 1992 was 73.5 years (E(0) = 73.5) and in 1996 was 75.7 years (E(4) = 75.7), we can calculate the slope as follows:
slope = (75.7 - 73.5) / (4 - 0) = 2.2 / 4 = 0.55
So, the slope (m) of the linear function is 0.55.
Next, we need to find the y-intercept (b) by substituting the values of one known point (t, E(t)) into the equation and solving for b. Let's use the point (0, 73.5):
73.5 = 0.55(0) + b
73.5 = b
So, the y-intercept (b) is 73.5.
Now we can determine the linear function E(t) that fits the data:
E(t) = 0.55t + 73.5
To predict the life expectancy of males in 2009 (t = 17), we can substitute t = 17 into the equation:
E(17) = 0.55(17) + 73.5 = 9.35 + 73.5 = 82.85
The predicted life expectancy of males in 2009 is approximately 82.85 years.
In summary:
E(t) = 0.55t + 73.5
E(17) = 82.85
To fill in the linear function E(t) that fits the data, we first need to determine the slope (rate of change) and the y-intercept.
To find the slope, we use the formula:
slope = (change in y) / (change in x)
In this case, the change in y represents the difference in life expectancy, and the change in x represents the number of years since 1992.
Substituting the values, we have:
slope = (75.7 - 73.5) / (1996 - 1992) = 2.2 / 4 = 0.55
So, the slope is 0.55.
To find the y-intercept, we can substitute one set of values into the equation E(t) = slope * t + y-intercept. Let's use the first data point from 1992:
73.5 = 0.55 * 0 + y-intercept
y-intercept = 73.5
Thus, the linear function E(t) that fits the data is:
E(t) = 0.55t + 73.5
To predict the life expectancy of males in 2009, we plug in the value t = 17 into the function:
E(17) = 0.55 * 17 + 73.5
E(17) = 9.35 + 73.5
E(17) = 82.85
Therefore, the predicted life expectancy of males in 2009 is 82.85 years.