Question

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
Use interpolation to estimate the percentage of children enrolled in 2011. (Round your answer to one decimal place.)

Answer 1

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,

$\frac{y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}$

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.

$\frac{y-63.7}{64.3-63.7} =\frac{3-2}{4-2}$.

$\frac{y-63.7}{0.6} =\frac{1}{2}$.

$y-63.7 =\frac{1}{2}(0.6).$

y-63.7=0.3.

y= 63.7+0.3

y= 64.

The percentage of children enrolled in 2011 is 64 %.