In 1994, the life expectancy of males in a certain country was 64.8 years. In 2000, it was 67.5 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994. E(t)=______ t + ______. Use the function to predict the life expectancy od males in 2003. E(9)=______.
Round both to the nearest tenth.
Life expectancy increases 0.45 years per year. I got that by dividing (67.5-64.8) by 6 years
E(t) = 64.8 + 0.45 t
2003 is year t = 9. Use the formula above to compute E(9)
To find the equation for E(t) representing the life expectancy in year t, we can use the slope-intercept form of a linear equation: y = mx + b. In this case, E(t) is equivalent to y, t represents the number of years since 1994 (which is equivalent to x), and the unknowns we need to find are m and b.
Given that the life expectancy of males in 1994 was 64.8 years and in 2000 it was 67.5 years, we can use these two points to calculate the slope (m).
Let's use the formula for the slope (m):
m = (y2 - y1) / (x2 - x1)
Plugging in the values:
m = (67.5 - 64.8) / (2000 - 1994)
m = 2.7 / 6
m = 0.45
Now that we have the slope (m), we can find the y-intercept (b) by substituting one of the given points (x, y) into the equation:
Using the point (1994, 64.8):
64.8 = 0.45 * 0 + b
64.8 = b
Therefore, b = 64.8.
Now we can write the equation E(t) = mt + b as:
E(t) = 0.45t + 64.8
To predict the life expectancy of males in 2003, we need to substitute t = 9 into the equation:
E(9) = 0.45 * 9 + 64.8
E(9) = 4.05 + 64.8
E(9) = 68.85
Rounded to the nearest tenth, the predicted life expectancy of males in 2003 is approximately 68.9 years.