In 1991, the life expectancy of males in a certain country was 70.4 years. In 1996, it was 72.9 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991. What is the linear function E(t) that fits the data?
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To find the linear function that fits the data, we need to determine the relationship between the life expectancy and the number of years since 1991. The linear function E(t) can be represented by the equation:
E(t) = mt + b
Where m represents the slope of the line and b represents the y-intercept.
To find the slope (m), we need to calculate the change in life expectancy (ΔE) divided by the change in years (Δt). In this case:
ΔE = 72.9 - 70.4 = 2.5
Δt = 1996 - 1991 = 5
m = ΔE / Δt = 2.5 / 5 = 0.5
So, the slope (m) is 0.5.
To find the y-intercept (b), we can substitute the values of any point (t, E) from the given data into the linear equation. Let's use the point (0, 70.4) since 1991 is the starting point.
E(t) = mt + b
70.4 = 0.5(0) + b
70.4 = b
So, the y-intercept (b) is 70.4.
Therefore, the linear function E(t) that fits the given data is:
E(t) = 0.5t + 70.4