Final answer:
To predict the price of Stock Texas when Bond Austin is worth $68.74, we use the constant of variation found from the initial prices ($3588 = 156 * 23). The equation for the inverse variation is $3588 = Stock Texas price * $68.74, which solves to a predicted Stock Texas price of approximately $52.22 per share.
Step-by-step explanation:
To predict the price of Stock Texas when Bond Austin is worth $68.74 using an equation modeling the inverse variation between the stock and bond prices, we start with the initial condition: the price of Stock Texas is $156 per share when Bond Austin is $23 per bond. This gives us the equation K = Stock Texas price * Bond Austin price, where K is the constant of variation. Plugging in the values, we get K = 156 * 23. To find the new price of Stock Texas when Bond Austin is $68.74, we use the equation K = Stock Texas price * $68.74. We then solve for the new Stock Texas price.
The constant of variation, K, calculated from the initial condition is $3588. The equation to predict the new price of Stock Texas is then $3588 = new Stock Texas price * $68.74. Solving this equation for the new Stock Texas price gives us a price of approximately $52.22 per share. Therefore, when Bond Austin is worth $68.74, Stock Texas is predicted to be priced at approximately $52.22 per share.