In1991,the life expectancy of males in a certain country was 72.6yrs. In 1996, it was 74.4 yrs. let E represent the life expectancy in year t and let t represent the number of years since 1991.

Question

In1991,the life expectancy of males in a certain country was 72.6yrs. In 1996, it was 74.4 yrs. let E represent the life expectancy 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 + ________
Round to the nearest tenth.

Answer 1

To find the linear function E(t) that fits the given data, we need to use the slope-intercept form of a linear equation, which is:

E(t) = mt + b

where m represents the slope and b represents the y-intercept.

To determine the slope, we can use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Let's use the given data:
(x₁, y₁) = (0, 72.6) represents the year 1991
(x₂, y₂) = (5, 74.4) represents the year 1996 (since 1991 + 5 years = 1996)

Substituting the values into the formula:

m = (74.4 - 72.6) / (5 - 0)
m = 1.8 / 5
m = 0.36

So, the slope, m, is 0.36.

Now, to determine the y-intercept, b, we can substitute one of the given data points into the equation and solve for b.

Let's use the point (0, 72.6) since it represents the year 1991:

72.6 = 0.36(0) + b
72.6 = b

So, the y-intercept, b, is 72.6.

Now, substituting the values of m and b into the equation E(t) = mt + b, we get:

E(t) = 0.36t + 72.6

Therefore, the linear function E(t) that fits the given data is:
E(t) = 0.36t + 72.6.

Answer 2

To find the linear function that fits the data, we need to determine the slope and the y-intercept of the line.

Given that the life expectancy in 1991 was 72.6 years (which corresponds to t=0), we can use this point to determine the y-intercept.

Let's use the point-slope form of a linear equation: y - y1 = m(x - x1).

Using the point (0, 72.6), we get:
E - 72.6 = m(t - 0)

Simplifying this equation, we have:
E = m(t - 0) + 72.6
E = mt + 72.6

Now we need to find the value of the slope, which represents the change in life expectancy per unit change in t. We can use the second data point from 1996 to calculate the slope.

Given that the life expectancy in 1996 was 74.4 years (which corresponds to t=5), we can substitute these values into the equation.

74.4 = m(5) + 72.6

Rearranging the equation to solve for m, we have:
m(5) = 74.4 - 72.6
5m = 1.8
m = 1.8/5
m = 0.36

Now that we have the value of the slope, we can substitute it back into the equation E = mt + 72.6:
E = 0.36t + 72.6

Therefore, the linear function that fits the data is E(t) = 0.36t + 72.6.