Chapter 4.4, Problem 15E

a.

To determine

To write: An equation that models the birthrate as a function of the number of years since $1960$ .

Answer to Problem 15E

The equation is $y=-0.308x+35.4$ .

Explanation of Solution

Given Information: A table showing the world birth rates $y$ (number of births per $1000$ people) $x$ years since $1960$.

Graph & Calculation:

Let us make a scatter plot of the given data.

  

Since the scatter plot shows a negative correlation, a line can be fitted to the data.

Using slope-intercept form to write equation utilizing two points $(0,35.4)$ and $(50,20)$ ,

  $y=mx+b$

  $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}m=\frac{20-35.4}{50-0}\\ m=-\frac{15.4}{50}\\ m=-\frac{154}{500}\\ m=-0.308\end{array}$

  $y-\mathrm{intercept}(b)=35.4$ $($ when $x=0$ $)$

  $y=-0.308x+35.4$

Thus, the equation is $y=-0.308x+35.4$ .

b.

To determine

To interpret: The slope and $y-\mathrm{intercept}$ of the line of fit.

Explanation of Solution

Given Information: A table showing the world birth rates $y$ (number of births per $1000$ people) $x$ years since $1960$ .

Interpretation:

The slope of the graph shows the rate of change in number of births which is decreasing at a rate of $0.308$ per year.

The $y-\mathrm{intercept}$ represents the number of births per every $1000$ people in $1960$ which is $35.4$ .