Question

The birth rate in a certain country in 1992 was 15.3 births per thousand population. In 2002, the birth rate was 15.09 births per thousand,a. Lot x represent years after 1992 and y represent the birth rate. Assume that the relationship between x and y is linear over this period. Write a linear equationthat relates y in terms of x.b. Use the linear equation from part (a) to estimate the birth rate in this country in the year 2012a. Determine the equation describing the linear relationship.y-O(Simplify your answer. Type your answer in slope-intercept form. Use integers or decimals for any numbers in the expression.)b. Use the equation from part (a) to determine the birth rate in the year 2012births per thousand population(Simplify your answer. Type an integer or a decimal.)

Answer 1

Check below, please.

1) To tackle this question we need to identify two points. Let 1992 be year 1 and 2002, be year 10. So we have (1, 15.3) and (10, 15.09)

2)

a)

So, we can write out the following to find the slope:

`m=(15.09-15.3)/(10-1)=-0.02333`

So let's make use of the slope-intercept form to check the value of "b":

`\begin{gathered} y=mx+b,m=-0.0233,(1,15.3) \\ 15.3=-0.02333(1)+b \\ b=15.3233 \end{gathered}`

Thus the linear equation is:

`y=-0.0233x+15.3233`

b) Now for the "b" part. Note that 2012 is 20 years after 1992. Therefore we can write out the following, plugging into x=20

`\begin{gathered} y=-0.0233x+15.3233 \\ y=-0.0233(20)+15.3233 \\ y=14.85 \end{gathered}`

So in 2012, the rate was 14.85 births per thousand people.