Linear functions problem?

[tanyas1976]

In 1994 the life expectancy of males in a certain country was 71.4 years. In 2001 it was 73.6 years. Let E represent the life expectancy in years t and let t represent the number of years since 1994.

*The linear function E (t) that fits the data is:
E(t)=__t+__ (round to the nearest tenth)

*Use the function to predict the life expectancy of males in 2005.
E(11)=__ (round to the nearest tenth)

 

[Deleted member 4993]

In 1994 the life expectancy of males in a certain country was 71.4 years. In 2001 it was 73.6 years. Let E represent the life expectancy in years t and let t represent the number of years since 1994.

*The linear function E (t) that fits the data is:
E(t)=__t+__ (round to the nearest tenth)

*Use the function to predict the life expectancy of males in 2005.
E(11)=__ (round to the nearest tenth)

And your work?!!

You have put up four probelms - without a line of work.

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[tanyas1976]

I do not show any work for this problem because I do not know how to begin to solve it. I am looking for guidance not answers. Thank you.

 

[mmm4444bot]

Let E represent the life expectancy in years t and let t represent the number of years since 1994.

The letter t (highlighted in red above) does not make sense, at that location in the sentence. So, delete it.

The linear function E(t) ... The word "linear" is a big clue. The graph is a straight line.

Are you familiar with the Slope-Intercept Form of an equation for a line?

That's what you need to find, for the first part of this exercise.

y = mx + b

Using function notation, they've changed the name of the dependent variable from y to E(t).

They've changed the name of the independent variable from x to t.

E(t) = m*t + b

You need to calculate the value of the slope m, and the y-intercept b.

You can do this from the two given coordinates: (0, 71.4) and (7, 73.6).

 

[tanyas1976]

okay...I'm still pretty confused with this one..I keep reading the breakdown of how to solve a problem like this one and I get so lost..

 

[mmm4444bot]

I'm still pretty confused with this one

Okay, let's forget about the context (for now), and just find the equation of the line that passes through the points (0, 71.4) and (7, 73.6).

A common form for a linear equation is: y = mx + b

The symbol m represents the line's slope.

Can you find the slope of the line in this exercise, using the two known points and the Slope Formula?

\(\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}\)

 

[tanyas1976]

okay...after much review and a huge headache..this is what I came up with:

73.6-71.4=2.2 2001-1994=7 2.2 divided by 7=.314

E(11)=.314(11)+71.4 ... See More

E(11)=74.85 E=74.85/11

E=6.8

final age is 74.8 years

I think this is right?

 

[mmm4444bot]

73.6-71.4=2.2 2001-1994=7 2.2 divided by 7=.314 Please do not type three equations on one line. It's confusing.

Type each equation on its own line.

E(11)=.314(11)+71.4 ... See More See more what?

E(11)=74.85 This is not properly rounded

E=74.85/11 E(11) does not mean E times 11, and we do not divide anything by 11, in this exercise.

E=6.8 Throw this line away.

final age is 74.8 years This is almost correct, but we're not asked for "final age", and it's not properly rounded.

You're on the right track, Tanya, but let's fix a few things.

We are told that the independent variable represents the number of years after 1994.

Therefore, t does not equal 1994 or 2005.

In 1994, t = 0
In 1995, t = 1
In 1996, t = 2
et cetera

However, when calculating the slope, it works out the same, so your value of 0.314 is okay.

Here is what I think that your instructor wants to see:

The two pairs of given (t, E(t)) coordinates on this line are (0, 71.4) and (7, 73.6)

m = (73.6 - 71.4)/(7 - 0)

m = 2.2/7

m = 0.314

E(t) - 71.4 = 0.314(t - 0)

E(t) = 0.314 t + 71.4

E(11) = 0.314(11) + 71.4

E(11) = 74.857

(Always report your final answer to a word problem using a complete English sentence.)

The model predicts that life-expectancy for males in 2007 is 74.9 years.