Question

The minimum amount of money, y, a bank guarantees an account holder will gain for a $2,000 deposit being compounded monthly for x years is represented by the inequality y≥2,000(1.045)x . The maximum balance of a $2,000 investment into a risky hedge fund is represented by the inequality y≤−16x2+96x+2,000 . On the graph of these two functions, the x-axis represents time, and the y-axis represents the investment balance. What does the shaded section represent?Select the correct answers from the lists.(1 point)The shaded section represents all the possible combinations of  and investment balances for which the stock provides a financial return for

Answer 1

The shaded section of the graph represents all the possible combinations of time (x) and investment balances (y) for which:

1. The bank guarantees a minimum balance from a safe investment account: This is represented by the inequality \( y \geq 2,000(1.045)^x \), illustrating that the balance will never go below this amount over time.

2. The risky hedge fund provides a maximum balance: This is captured by the inequality \( y \leq -16x^2 + 96x + 2,000 \), which shows the upper limit of expected returns for that investment.

Thus, the shaded area between these two curves represents the "possible balances" for investments that fall within the range where the hedge fund might provide returns greater than what the bank guarantees as the minimum. Essentially, the shaded region indicates the potential outcomes of the hedge fund investment that are still above the guaranteed bank balance.

So, to summarize, the shaded section represents all the possible combinations of time (x) and investment balances (y) for which the hedge fund provides a financial return that is above the guaranteed minimum of the bank investment.