Question

At the end of the summer, Caitlin had saved $120 from her summer job. This was her initial deposit into a new savings account at the bank. As the school year starts, Caitlin is going to deposit another $5 each week from her allowance. Is her account balance proportional to the number of weeks of deposits? Explain your reasoning.

Answer 1

Yes, Caitlin's account balance is proportional to the number of weeks of deposits. For every additional week, her account balance will increase by $5.

Step-by-step explanation:

Yes, Caitlin's account balance is proportional to the number of weeks of deposits.

To understand why, let's look at the scenario. Caitlin initially deposited $120 into her savings account. Each week, she deposits an additional $5 from her allowance. Since she deposits the same amount every week, we can say that the rate of deposit is consistent and constant.

When we graph Caitlin's account balance over time, with the number of weeks on the x-axis and the account balance on the y-axis, we will get a straight line. This indicates a direct variation, where the account balance is directly proportional to the number of weeks of deposits. For every additional week, Caitlin's account balance will increase by $5. So, if she deposits for 5 weeks, her account balance will be $120 + (5 * $5) = $145. If she deposits for 10 weeks, her account balance will be $120 + (10 * $5) = $170, and so on.