The minimum amount of money, y, a savings & loan guarantees an account holder will gain for a $750 deposit being compounded monthly for x years is represented by the inequality y≥600(1.05)x

Question

. The maximum balance of a $600 investment into a penny stock is represented by the inequality y≤−12x2+90x+600
. 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?(1 point)
Responses

The shaded section represents all the possible combinations of time and investment balances for which the penny stock provides a greater financial return for the $500 investment.
The shaded section represents all the possible combinations of time and investment balances for which the penny stock provides a greater financial return for the $500 investment.

The shaded section represents all the possible combinations of time and investment balances for which the penny stock provides a lesser financial return for the $600 investment.
The shaded section represents all the possible combinations of time and investment balances for which the penny stock provides a lesser financial return for the $600 investment.

The shaded section represents all the possible combinations of time and investment balances for which the penny stock provides a greater financial return for the $600 investment.
The shaded section represents all the possible combinations of time and investment balances for which the penny stock provides a greater financial return for the $600 investment.

The shaded section represents all the possible whole number combinations of time and investment balances for which the penny stock provides a greater financial return for the $600 investment.

Answer 1

To analyze the problem, we have two inequalities representing different investment options.

1. The first inequality, \( y \geq 600(1.05)^x \), models the amount guaranteed by the savings & loan account for a $750 deposit compounded monthly over \( x \) years.

2. The second inequality, \( y \leq -12x^2 + 90x + 600 \), models the maximum balance of a $600 investment into a penny stock over \( x \) years.

The shaded section of the graph will be the area that satisfies both inequalities simultaneously.

• The area above the curve defined by the savings & loan account (the first function) represents the balances that are equal to or greater than what the savings provides.
• The area below the curve defined by the penny stock investment (the second function) represents balances that are less than or equal to what the penny stock can return.

Therefore, when you combine these inequalities, the shaded section would represent values of \( y \) that indicate the investment balance is higher than the savings account balance but simultaneously lower than the maximum possible for the penny stock.

From the options given, the best and correct interpretation of the shaded section is:

The shaded section represents all the possible combinations of time and investment balances for which the penny stock provides a lesser financial return for the $600 investment.

This option correctly highlights that the values in the shaded area reflect situations where the balance from the penny stock investment is less than that from the savings & loan investment.