Respuesta :
The percentage of children enrolled in 2011 is 64 %.
Step-by-step explanation:
From the given data we are given with set of x values an y values.
Moreover, the years were given with differences of 2 years.
So let us consider the years 2008 as 0, 2010 as 2, 2012 as 4 and 2014 as 6.
Using interpolation we have to find the percentage of children enrolled in 2011. i.e. 3.
Interpolation is given by the formula,
[tex]\frac{y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}[/tex]
Let us choose the points (2, 63.7) and (4, 64.3), since 3 is between 2 and 4.
Substitute the values in the formula.
[tex]\frac{y-63.7}{64.3-63.7} =\frac{3-2}{4-2}[/tex].
[tex]\frac{y-63.7}{0.6} =\frac{1}{2}[/tex].
[tex]y-63.7 =\frac{1}{2}(0.6).[/tex]
y-63.7=0.3.
y= 63.7+0.3
y= 64.
The percentage of children enrolled in 2011 is 64 %.
The percentage of children enrolled in 2011 with the help of interpolation formula is 64%.
What are ratio and proportion?
A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
The following table shows the percentage of children in the United States between the ages of 3 and 5 who are enrolled in preprimary programs.
Date 2008 2010 2012 2014
Percentage 63.0 63.7 64.3 64.7
The difference of years is 2.
Then by the interpolation, we have
[tex]\rm \dfrac{y-y_1}{y_2-y_1} = \dfrac{x-x_1}{x_2-x_1}[/tex]
Let us take the points (2, 63.7) and (4, 64.3). Then for x = 3, we have
[tex]\begin{aligned} \dfrac{y-63.7}{64.3-63.7} &= \dfrac{3-2}{4-2}\\\\y - 63.7 &= 0.3\\\\y &= 64 \end{aligned}[/tex]
The percentage of children enrolled in 2011 is 64%.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
