Question

William wants to choose between two five-year investment plans. In plan I, he is required to make a one-time investment of $12,000 and then equal monthly investments of $400. For plan II, the function y = 11,000 + 420 represents the total amount in dollars, y. Wiliam will have invested in relation to the number of months elapsed. x.

Which statements about the functions for the two investment plans are true? ( choose more than one answer)

The functions are both increasing.

The functions are both decreasing.

The function for plan I has a greater unit rate.

The function for plan II has a greater unit rate.

The function for plan I has a greater y-intercept.

The function for plan II has a greater y-intercept.

Answer 1

William is evaluating two investment plans: Plan I, with a $12,000 initial investment and $400 monthly, is represented by y = 400x + 12,000; Plan II is y = 11,000 + 420x. Both investment functions are increasing, Plan I has a greater y-intercept, and Plan II has a greater unit rate.

Step-by-step explanation:

William is trying to decide between two five-year investment plans. In plan I, a one-time investment of $12,000 is needed, followed by equal monthly investments of $400. This can be represented by the linear function y = 400x + 12,000. Plan II is already given by the function y = 11,000 + 420x, where y is the total amount invested and x is the number of months.

When comparing the two investment functions, we can make the following true statements:

• The functions are both increasing, as both have positive unit rates (slopes).
• The function for plan I has a greater y-intercept ($12,000 compared to $11,000 for plan II).
• The function for plan II has a greater unit rate ($420 per month compared to $400 per month for plan I).

Thus, over time, plan II's total investment grows faster due to a higher monthly investment amount, even though it starts with a slightly lower initial investment.