How to solve this word problem?

Question

1.In 1960,the life expectancy of Filipino males 51 years,while in 1970 it was 55 years.
a.) Write E, the life of expectancy,as a linear function of t, the number of years since 1960. [Hint: Use(0,51) and (10,55) as data points]
b.)Use the equation in (a) to predict the life expectancy of males in 2010.

Answer 1

a) The form of a linear equation is...

y = mx + c

where m is the gradient (slope) of the line and c is the y intercept (where the line cuts the y axis or what y is when x is 0).

Your problem asks you to create a similar equation (in terms of E and t).

E = mt + c

The gradient is given by dy/dx (the change in y / the change in x). Since you know two points on the line (0,51) and (10,55), you can calculate the gradient (m).

(55 - 51) / (10 - 0) = 4/10 or 0.4
(change in y) / (change in x)

So we have...

E = 0.4t + c

c is what y will be when x is 0. We know the point (0, 51) so c will be 51. So your final linear equation is...

E = 0.4t + 51

b) We need to know life expectancy in 2010 (or 50 years after 1960) so substitute 50 in for t to get E...

E = 0.4 * 50 + 51
E = 20 + 51
E = 71

So, assuming (and that's a very big assumption) that life expectancy in Filipino males grows linearly, men in the Phillippines will be living to 71 on average by 2010.

Hope that makes sense!!

Answer 2

E = 0.4 t + 51

2010, t = 50

E = 71

Answer 3

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