SOLUTION: In 1991 the life expentancy of males were in a certain country was 68.5 years. In 1996 it was 71.1 years. Let E represent the lif expenctancy in year t, and let t represent the nu

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Question 142655: In 1991 the life expentancy of males were in a certain country was 68.5 years.
In 1996 it was 71.1 years. Let E represent the lif expenctancy in year t, and let t represent the number of years since 1991.
The linear function E(t)that fits the data is
E(t)=?t + ??
Use the function to predict the life expendancy of males in 2009.
E(18)=
Can someone please help me with this I have no idea where to even start. I dont understand these at all, will someone explain to me or at least try to help me??
Answer by marcsam823(57) About Me  (Show Source):
You can put this solution on YOUR website!
First of all let's remove the question marks and re-write the equation with some letters. The problem states that the equation is linear which means it graphs as a line with a slope and y-intercept. Let's call the slope "m" and the y-intercept "b". Our re-written equation is therefore:
E%28t%29+=+mt+%2B+b
where t is equal to the number of years that have passed since 1991. For example:
1991: t = 0 (no time has passed)
1992: t = 1 (one year has passed), etc.
1993: t = 2
.
.
.
2009: t = 18
What we will do in this problem is construct an equation based on the data provided. The 1991 data will help us solve for "b" in our equation and the 1996 data will aid us in finding the slope "m". After that, it's just a matter of plugging in values for t to find E(t) or vice versa.
Step 1:
Find "b":
In our problem, 1991 is the first year data was recorded so t+=+0 and the life expectancy is 68.5 years.
Therefore:
E%280%29+=+m%280%29+%2B+68.5
E%280%29+=+68.5
68.5 is the baseline age. Based on the data provided in the problem we expect the life expectancy to increase as the value for t increases.
Our equation now looks like this:
E%28t%29+=+m%28t%29+%2B+68.5
Step 2:
Find "m":
We are given that in 1996 the life expectancy increased to 71.1. Since 1996 is five years after 1991:
t+=+5
E%285%29+=+71.1
E%28t%29+=+m%28t%29+%2B+68.5
E%285%29+=+m%285%29+%2B+68.5
71.1+=+5m+%2B+68.5
5m+=+2.6
m+=+.52
This means that every time t increases by one the life expectancy increases by .52 years (or about 1/2 year or 6 months)
Our equation now looks like this:
E%28t%29+=+.52t+%2B+68.5
Step 3:
Find the life expectancy in 2009
Since we now have an equation all we need to do for this step is determine the value of t
Since 2009+-+1991+=+18, t+=+18
Let's plug this value into the equation:
E%28t%29+=+.52t+%2B+68.5
E%2818%29+=+.52%2818%29+%2B+68.5
E%2818%29+=+9.36+%2B+68.5
E%2818%29+=+77.86
or approximately 78 years life expectancy
You can now plug in any value for t and find E(t) or any value for E(t) and find t.