Question

Some banks chargea fee on saving accounts that are left inactive for an extended period of time. The equation y=5,000(0.98)x represents the value, y, of one account that was left inactive for a period of x years. What is the y-intercepts of this equation and what does it represent?

A 0.98 the percent of money in the account initially
B 0.98, the percent of money in the account after x years
C 5,000, the amount of money in the account initially
D 5,000, the amount of money in the account after x years.

Answer 1

C 5,000, the amount of money in the account initially. The y-intercept of the equation is 5,000, which represents the initial amount of money in the savings account before any inactivity fees are deducted over time. Option C correctly describes the y-intercept as being the initial sum in the account.

Step-by-step explanation:

The y-intercept of the equation y=5,000(0.98)x represents the value of the savings account when x, the number of years, is zero. By substituting x with 0, the value of y is the initial amount in the account, since any number raised to the power of zero is 1. Hence, y = 5,000(0.98)0 = 5,000(1) = 5,000. This indicates that the y-intercept is 5,000. This value represents the amount of money in the account initially before any inactivity fees are applied over the years.

Looking at the given options for what the y-intercept represents, option C, which states that 5,000 is the amount of money in the account initially, is correct. Option B refers to 0.98 as the percent of money in the account after x years; however, this is actually the rate at which the money decreases due to fees every year, not the percent remaining.