Q13. - Algebra 2

Question

For exercise 13 and 14, use the following information.

Della has $1000 that she wants to invest in the stock market. She is considering buying stock in either Company 1 or Company 2. The values of the stocks at the ends of the last four months are shown in the tables below:

13. Based only on these data, which stock should Della buy? Explain.

Step-by-Step Solution

Answer

Della should buy Company 2 stock.

Step-1 – Prediction equation for company 1.

Consider the data for October and November for the Company 1.

Let x is the number of months since August.

The share price in October was $24.19$ and in November was $22.56$.

The above information can be written as $(2,24.19) and (3,22.56)$.

Put $(x_1,y_1)=(2,24.19) and (x_2,y_2)=(3,22.56)$ into the formula $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$.

$\begin{array}{l}y-24.19=\frac{22.56-24.19}{3-2}(x-2)\\ y-24.19=-1.63(x-2)\\ y=-1.63+27.45\end{array}$

Step-2 – Prediction equation for company 2.

Consider the data for October and November for the Company 2.

The share price in October was $32.06$ and in November was $32.44$.

The above information can be written as $(2,32.06) and (3,32.44)$.

Put $(x_1,y_1)=(2,32.06) and (x_2,y_2)=(3,32.44)$ into the formula $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$.

$\begin{array}{l}y-32.06=\frac{32.44-32.06}{3-2}(x-2)\\ y-32.06=0.38(x-2)\\ y=0.38x+31.3\end{array}$

Step-3 – Determine the stock.

Here we can observe that company 2 has positive slope and it suggests that the value of company 2’s stock is going up.

Thus, Della should buy Company 2 stock.