# Video: Solving Word Problems Involving Rate of Change

Daniel opened a savings account with \$145. Every month, he made the same deposit and made no withdrawals. After 3 months, he had \$214. After 6 months, he had \$352. After 9 months, he had \$559. Determine the rate of change in his savings account.

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### Video Transcript

Daniel opened a savings account with 145 dollars. Every month, he made the same deposit and made no withdraws. After three months, he had 214 dollars. After six months, he had 352 dollars. After nine months, he had 559 dollars. Determine the rate of change in his savings account.

When Daniel opened up his account at month zero, he had 145 dollars. And it says after three months — one, two, three — he had 214 dollars. Then after six months, one month, two, three, four, five, six, he had 352 dollars. Then after nine months, he had 559 dollars. Determine the rate of change in his savings account.

To find the rate of change, we need to take the change in money and divide it by the change in time. Let’s begin for months zero to three. Three months went by because three minus zero is three. Now, to find the change in money, we need to take 214 dollars and subtract 145 dollars. And we get 69 and then divide it by three, we get 23. So what does that mean? His savings account is growing by 23 dollars per month.

Now, let’s go ahead and check our other deposits. So instead of looking for months zero to three, how about for months three to nine? From months three to nine, six months went by, which we would get from taking nine minus three to be six. And then the money, we would find that change by taking 352 minus 214. 138 divided by six and we get 23. So he is depositing every month the same amount. That must be 23 dollars.

Now, to triple check, let’s take a look at months nine to 18. That’s a nine-month difference. Since 18 minus nine is nine. And now we subtract 352 dollars from 559 dollars. And 207 divided by nine is once again 23. Therefore, the rate of change in his savings account is 23.