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 + 420x represents the total amount in dollars, y, William will have invested in relation to the number of months elapsed, x. Which statements about the functions for the two investment plans are true? 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

Both investment plans have increasing functions. Plan II has a greater unit rate of $420 per month versus Plan I's $400 per month. Plan I has a greater initial investment with a y-intercept of $12,000, compared to Plan II's $11,000.

Step-by-step explanation:

To compare the two investment plans for William, we need to understand the structure of each plan and recognize that the function for each plan represents how the total investment grows over time. Plan I requires an initial investment of $12,000 with an additional $400 invested every month.

Plan II is represented by the function y = 11,000 + 420x, where y is the total amount invested and x is the number of months.

The functions for both plans are increasing, as additional money is added over time.

The function for plan II has a greater unit rate of $420 per month, compared to Plan I's $400 per month.

The function for plan I has a greater y-intercept at $12,000, as opposed to Plan II's y-intercept at $11,000. This means Plan I starts with a higher initial investment.

Answer 2

The functions are both increasing