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)=____
unsure what to do here I do not get the question.
You are making a linear math model for life expectancy.
slope= (75.7-73.5)/73.5
e(t)=slope*t+b
b will equal 73.5 check that.
To find the slope would it then be 75.7-73.5/73.5
so the slope would be 33.4?
To find the linear function E(t) that fits the given data, we need to determine the equation in the form E(t) = mt + b, where m is the slope of the line and b is the y-intercept.
We are given two data points:
1. In 1992 (t = 0), the life expectancy was 73.5 years (E = 73.5).
2. In 1996 (t = 4), the life expectancy was 75.7 years (E = 75.7).
To find the slope, m, we can use the formula:
m = (E2 - E1) / (t2 - t1)
Substituting the values:
m = (75.7 - 73.5) / (4 - 0)
m = 2.2 / 4
m = 0.55
Now that we have the slope, we can use one of the data points to find the y-intercept, b.
Using the point (t = 0, E = 73.5) in the equation E(t) = mt + b:
73.5 = 0.55(0) + b
73.5 = b
Therefore, the equation for the linear function E(t) is:
E(t) = 0.55t + 73.5
To predict the life expectancy of males in the year 2009 (t = 17), we can use the equation E(t) = 0.55t + 73.5:
E(17) = 0.55(17) + 73.5
E(17) = 9.35 + 73.5
E(17) = 82.85
Hence, the predicted life expectancy of males in 2009 would be 82.85 years.