in 1990 the life expectancy of males in a certain country was 64.7 years. In 1994 it was 67.3 let E represent the life expectancy in year t and let t represent the number of years since 1990.
What is the linear function E(t) that fits the data? what would the life expectancy of males be in 2009?
not quite enough information.
Is the increase linear or exponential?
In either case, treat your data as two ordered pairs
(0,64.7) and (4,67.3)
If linear :
slope = .65 , y-intercept is 64.7
then E = .65t + 64.7
for 2009 , t = 19
E(19) = .65(19) + 64.7 = 77
If exponential, let
E(t) = 64.7(e)^(kt)
for (4,67.3)
67.3 = 64.7e^(4k)
1.040185 = e^(4k)
4k = ln(1.040185)
k = .00985
E(t) = 64.7e^(.00985t)
E(19) = 78
(This data seems unreasonable. It would be impossible to raise the life expectancy by almost 15 years in less than 20 years)
math
To find the linear function that fits the given data, we can use the slope-intercept form of a linear equation, which can be written as:
E(t) = mt + b
where t represents the number of years since 1990, E(t) represents the life expectancy in year t, m represents the slope of the line, and b represents the y-intercept of the line.
Given that the life expectancy in 1990 is 64.7 years (when t = 0) and the life expectancy in 1994 is 67.3 years (when t = 4), we can use these two data points to find the slope (m) and the y-intercept (b) of the linear function.
We can start by calculating the slope (m) using the formula:
m = (E(t2) - E(t1)) / (t2 - t1)
Here, t1 is 0 (1990) and E(t1) is 64.7, while t2 is 4 (1994) and E(t2) is 67.3. Plugging these values into the formula, we get:
m = (67.3 - 64.7) / (4 - 0)
= 2.6 / 4
= 0.65
Now that we have the slope (m), we can find the y-intercept (b) by substituting the values of a known data point into the equation E(t) = mt + b. Let's use the data point from 1990 (t = 0, E(t) = 64.7):
64.7 = 0.65 * 0 + b
b = 64.7
So, the linear function E(t) that fits the given data is:
E(t) = 0.65t + 64.7
To find the life expectancy of males in 2009 (t = 19, as it is 19 years since 1990), we substitute t = 19 into the equation E(t) = 0.65t + 64.7:
E(19) = 0.65 * 19 + 64.7
= 12.35 + 64.7
= 77.05
Therefore, the life expectancy of males in 2009 would be approximately 77.05 years.