Chapter 1.1, Problem 19E

Solution

To Check:

That either one of the expressions $100\times L_2/L_1\to L_3$ or $L_3=100\left(L_2/L_3\right)$ when typed into the calculator causes the calculator to divide each entry of list $L_2$ by the corresponding entry in list $L_1$ , then multiplies the result by $100$ and then stores the resulting percentages in new list $L_3$ .

The expression $100\times L_2/L_1\to L_3$ causes a syntax error in the calculator.

The expression $L_3=100\left(L_2/L_1\right)$ when typed in the calculator appears in the form $L_3=100\cdot \frac{L_2}{L_1}$ after submission and causes the calculator to divide each entry of list $L_2$ by the corresponding entry in list $L_1$ , then multiplies the result by $100$ and then stores the resulting percentages in new list $L_3$ .

Given:

The table:

Year	Total	Male	Female
1965	102	98	4
1970	144	138	6
1975	90	85	5
1980	85	78	7
1985	94	84	10
1990	91	79	12
1995	73	62	11
2000	66	56	10
2005	69	58	11
2010	79	65	14
2015	79	64	15

List $L_1$ is has entries from the column with header “Total” in the above table.

List $L_2$ has entries from the column with header “Female” in the table above.

Concepts Used:

The list algebra techniques in the Geogebra Calculator.

Calculations:

The list $L_1$ is $\left\{102,144,90,85,94,91,73,66,69,79,79\right\}$ .

The list $L_2$ is $\left\{\text{4, 6, 5, 7, 10, 12, 11, 10, 11, 14, 15}\right\}$ .

Check the third and seventh entry from the lists as an example.

The third entry for $L_2$ is $5$ and that for $L_1$ is $90$ . The calculated value of the third entry for $L_3=100\left(L_2/L_1\right)$ should be:

  $\begin{array}{c}100\left(L_2/L_1\right)=100\left(5/90\right)\\ =\frac{50}{9}\\ \approx 5.5556\end{array}$

The seventh entry for $L_2$ is $11$ and that for $L_1$ is $73$ . The calculated value of the seventh entry for $L_3=100\left(L_2/L_1\right)$ should be:

  $\begin{array}{c}100\left(L_2/L_1\right)=100\left(11/73\right)\\ =\frac{1100}{73}\\ \approx 15.0685\end{array}$

Now try the expressions $100\times L_2/L_1\to L_3$ and $L_3=100\left(L_2/L_3\right)$ as input to the calculator and check if the third and seventh values match the above calculated values.

  

The expression $100\times L_2/L_1\to L_3$ causes a syntax error in the calculator.

The expression $L_3=100\left(L_2/L_3\right)$ gives $L_3$ as $\left\{\text{3}\text{.9216, 4}\text{.1667, 5}\text{.5556, 8}\text{.2353, 10}\text{.6383, 13}\text{.1868, 15}\text{.0685, 15}\text{.1515, 15}\text{.942, 17}\text{.7215, 18}\text{.9873}\right\}$ .

Note that the third element and the seventh element is same as calculated above.

Conclusion:

The expression $100\times L_2/L_1\to L_3$ causes a syntax error in the calculator.

The expression $L_3=100\left(L_2/L_3\right)$ when typed in the calculator appears in the form $L_3=100\cdot \frac{L_2}{L_1}$ after submission and causes the calculator to divide each entry of list $L_2$ by the corresponding entry in list $L_1$ , then multiplies the result by $100$ and then stores the resulting percentages in new list $L_3$ .