Question

Chuck chooses an investment plan that requires him to make a one-time investment of $10,000, and then equal monthly investments of $350 for the next 5 years. The function y = 10,000 + 350x represents the total amount in dollars Chuck will have invested, y, in relation to the number of months elapsed, x. Which statements about this function are true? The function is a linear function. The function is a nonlinear function. The function is an increasing function. The function is a decreasing function. The function changes at a constant rate.

Answer 1

Let's analyze the given function (y = 10,000 + 350x) and evaluate each statement:

1. The function is a linear function.

- True. The function is linear because it has a constant rate of change (the coefficient of (x), which is 350, is constant).

2. The function is a nonlinear function.

- False. The function is linear, not nonlinear.

3. The function is an increasing function.

- True. As (x) (the number of months) increases, the total amount invested (y) increases. The coefficient of (x) (350) is positive, indicating an upward slope.

4. The function is a decreasing function.

- False. The function is not decreasing; it is increasing over time.

5. The function changes at a constant rate.

- True. The coefficient of (x) (350) represents the constant rate of change. Chuck is making equal monthly investments, so the function changes at a constant rate.

In summary:

- The function is linear.

- The function is increasing.

- The function changes at a constant rate.