I have no clue, cause they haven't taught us!

[maidhoffhouse11]

I am having difficulty understanding this problem. We have not discussed nor learned how at all to solve these kinds of problems, and they want us to complete it for this test today! I am very frustrated. Is there anyone who can help me or explain to me how I would figure this out?

In 1995, the life expectancy of males in a certain country was 69.4 years. In 1999, it was 71.9 years. Let E represent the life expectancy in t and let t represent the number of years since 1995.

The linear E(t) that fits the data is
E(t)=?t+? <------I have no clue how to figure this out.
(round to the nearest tenth)

Use the function to predict the life expectancy of males in 2003.
E(8)=? <-------I have no clue where they got 8.
(round to the nearest tenth)

 

[tkhunny]

1995 is the base year and corresponds to E(0).

1999 corresponds to E(1999-1995) = E(5)

2003 corresponds to E(2003-1995) = E(8)

It's called an index.

It appears that a linear estimate is required. You have two points: (0,69.4),(5,71.9)

Let's see what you get.

 

[mmm4444bot]

We have not discussed nor learned how at all to solve these kinds of problems

A linear function has the form y = mx + b, where m is the slope.

Did you learn this?


To calculate the slope m from the coordinates of two known points, there is a Slope formula:

m = (difference of y coordinates)/(difference of x coordinates)

Did they teach you this?


If you have coordinates for one point on the line AND you know the slope, then you can write a linear function using something called the Point-Slope formula:

y - y[sub:12rc0tri]1[/sub:12rc0tri] = m(x - x[sub:12rc0tri]1[/sub:12rc0tri], where the known coordinates are (x[sub:12rc0tri]1[/sub:12rc0tri], y[sub:12rc0tri]1[/sub:12rc0tri])

Did they teach this?


These three things make up the foundation of what you need to know for this exercise.

The remaining part is for you to make the connection between this knowledge and the information given in the word problem.

That stated information is enough for you to write down the coordinates of two points on the line that is the graph of function E. Once you know the points, you can determine mt + b.

In this word problem, instead of y = mx + b, we are using the notation E(t) = mt + b. It's exactly the same thing; only some symbol names have changed.

The name x is called t, in this exercise.

The name y is called E(t) in this exercise.

t represents the number of years since 1995, so t = 0 in 1995; t = 1 in 1996, t = 2 in 1997, et cetera.

E(t) represents the life expectancy t years after 1995.

They tell you that E(t) = 71.9 when the year is 1999, so you need to put "two and two together" and reason on your own that this information represents the point (4, 71.9).

Likewise, when they tell you that E(t) = 69.4 for the year 1995, then you need to realize that the point (0, 69.4) is also on the line.

That's enough data to calculate the slope m and then to use the Point-Slope formula (or other method you know) to write the equation for the line.

Once you know the equation, you can calculate the value of E(t) for any value of t.

If you would like more help, please ask specific questions or show your work.

Cheers

 

[mmm4444bot]

E(t)=?t+? <------I have no clue how to figure this out.
(round to the nearest tenth)

E(t) = mt + b

Find m and b from implicitly-given data points.



E(8)=? <-------I have no clue where they got 8.

2003 is eight years after 1995; hence, t = 8 in the year 2003

This post is my short response.

 

[maidhoffhouse11]

Thank you all for your help, as I can see that this website and its members are going to be great to communicate with! I did manage to pass my quiz, I now can't recall the exact answer I got as it was Sunday, but I do recall that I got this answer correct. Again, thank you all.