Question

The table shows the average life expectancy at birth(in years) for a person born in the United States inthe indicated year. Use the table to answerquestions 5 and 6.Years after 195001020304050Life Expectancy 68.2 | 69.7 | 70.8 73.7 | 75.4 | 77.05. (MD1) Which equation best models thegiven data?

Answer 1

5)

Before we see which model best fits the given data, let's plot the points into a graph, that's fundamental! Always plot the points for better visualization, only by plotting the points we can see what kind of model we will use, then, plotting these points we will get:

Here, we are using the y-axis as the life expectancy and the x-axis as the years after 1950. Only looking at the graph we can see that the points follows something like a line, therefore, we are looking for a linear model, like

`y=ax+b`

But what value of "a" and "b" best fits the points? We can find it, but it will take a lot of time and calculus, then, let's look at the graph and see which equation in the option is correct. We only have two options for linear models:

`\begin{gathered} y=0.183x+67.895 \\ \\ y=67.895x+0.183 \end{gathered}`

To see which one is correct we just look at the y-intercept (number without "x"), looking at our graph the y-intercept is something like 68.2, then, the correct answer is

`y=0.183x+67.895`

The final answer for 5) is the letter C.

`y=0.183x+67.895`

6)

Now we can use the equation of 5) to find it, let's find the value of x that we will input into the function, 1995 is 45 years after 1950, then, we will input x = 45.

`\begin{gathered} y=0.183x+67.895 \\ \\ y=0.183\cdot(45)+67.895 \\ \\ y=8.235+67.895 \\ \\ y=76.13\text{ years old} \end{gathered}`

The predicted life expectancy for 1995 is 76.13 years old