I am lost, and I bet it is simple, but I have been working with many problems and I keep coming back to this and I grow increasingly confused. How do I begin to solve this problem?
In 1993 the life expectancy of males in a certain country was 71.7 years. In 1997 it was 75.2 years. Let E represent the life expectancy in years t and let t represent the number of years since 1993
E(t)=_t+ _
Use the formula below to predict the life expectancy of males in 2004
E (14) =
Already answered elsewhere. This is a duplicate post
To solve this problem, you are given that the life expectancy of males in a certain country was 71.7 years in 1993 and 75.2 years in 1997. You are asked to use a formula to predict the life expectancy in 2004.
First, let's analyze the given information. You are given two data points: (1993, 71.7) and (1997, 75.2). The first number in each data point represents the year, and the second number represents the life expectancy in that year.
To find the equation, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, we need to find the slope (m) and the y-intercept (b) to come up with the equation that predicts the life expectancy in a given year.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
We can choose (1993, 71.7) as (x1, y1) and (1997, 75.2) as (x2, y2):
m = (75.2 - 71.7) / (1997 - 1993)
m = 3.5 / 4
m = 0.875
So, the slope (m) is 0.875.
Now, let's find the y-intercept (b) using the formula:
b = y - mx
We can choose any data point to find the y-intercept. Let's use (1993, 71.7):
b = 71.7 - (0.875 * 1993)
b = 71.7 - 1743.375
b = -1671.675
So, the y-intercept (b) is -1671.675.
Now that we have the slope (m = 0.875) and the y-intercept (b = -1671.675), we can write the equation for life expectancy as a function of years since 1993 (t):
E(t) = 0.875t - 1671.675
To predict the life expectancy in 2004, we can substitute t with 14 (since 2004 is 14 years after 1993):
E(14) = 0.875 * 14 - 1671.675
E(14) = 12.25 - 1671.675
E(14) = -1659.425
Therefore, the predicted life expectancy of males in 2004 is approximately -1659.425 years.