Question

John opens a savings account with an initial deposit of $2000. He deposits $35 each week. Mary's savings account is represented by the function y = $45x + $2800 , where y is the balance of Mary's savings account after her initial deposit and a number of weekly deposits, x. Which statement BEST compares the rate of change for the two accounts?

A) Mary deposited $800 less than John.
B) John deposits $10 more each week than Mary.
C) John deposits $10 less each week than Mary.
D) Mary deposits $7 for every $9 John deposits.

Answer 1

The answer is C.

John’s savings account equation would be y=35x + 2000 while Mary’s is y=45x + 2800.
By comparing them, we see that Mary deposits 10 more than John per week.

Answer 2

The statement that best compares the rate of change for the two accounts is:

• C) John deposits $10 less each week than Mary.

Explanation:

In the equation that determines Mary's savings account balance:

• y = $ 45x + $ 2800

It can be identified that the $ 2800 mentioned is the initial deposit with which the savings account was opened, so the value of $ 45 is the weekly moment that Mary saves week after week, which will be increased once the variable X increase, considering that John's weekly savings amount is $ 35, it is valid to state that John saves $ 10 less than Mary since:

• $ 45 (amount saved by Mary) - $ 35 (Amount saved by John) = $ 10.