Please help with this word problem

Question

In 1994​, the life expectancy of males in a certain country was 73.2 years. In 2000​, it was 76.4 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994.

Determine the linear function​ E(t) that fits the data. Use the function to predict the life expectancy of males in

2005.

Answer 1

Jade

In 1994, t=0 and E(t) = 73.2

In 2000, t = 6, and E(t) = 76.4

So we have 2 points on our linear function (0,73.2) and (6, 76.4)

So if E(t) = mt + c

E(0) = 73.2, giving c = 73.2

E(6) = 6m + 73.2 = 76.4, giving m = 0.53

So E(t) = 0.53 t + 73.2

To find life expectancy in 2005, you need E(11).

Mike

Answer 2

We can use the 2 data points given to find the linear equation.

(0,73.2) and (6,76.4)

First find the slope.

(76.4-73.2)/(6-0) = 8/15

The y intercept is 73.2 (given in the problem don't have to calculate)

Bringing these together gives the equation of the line

E(t) = 8/15t+73.2

For 2005, t=11, plug this into the equation

E(11) = 8/15(11)+73.2

79.07