Question

. Joe makes a one-time deposit of $5,000.00 to open an interest-bearing savings account for his newborn grandson, Tyler. The table shows the expected balance of the account, , when Tyler is t years old. Age in years, Balance in dollars, 0 5,000.00 2 5,030.08 4 5,060.34 6 5,090.78 8 5,121.41 10 5,152.21 12 5,183.21 14 5,214.39 Consider five intervals representing periods of t years during which the account balance, , changed. Order the intervals from greatest to least average rate of change.

Answer 1

The intervals should be ordered from greatest to least average rate of change as follows: Interval 12-10, Interval 8-6, Interval 14-12, Interval 10-8, Interval 6-4.

Step-by-step explanation:

The question asks to order the intervals representing periods of time from greatest to least average rate of change. In this case, the intervals are represented by the ages of Tyler. We can calculate the average rate of change by finding the difference in balance for each interval and dividing it by the difference in years. The greater the average rate of change, the higher the interval should be ranked. Let's calculate the average rate of change for each interval:

1. Interval 14-12: Average rate of change = (5214.39 - 5183.21)/(14 - 12) = 15.09
2. Interval 12-10: Average rate of change = (5183.21 - 5152.21)/(12 - 10) = 16
3. Interval 10-8: Average rate of change = (5152.21 - 5121.41)/(10 - 8) = 15.9
4. Interval 8-6: Average rate of change = (5121.41 - 5090.78)/(8 - 6) = 15.82
5. Interval 6-4: Average rate of change = (5090.78 - 5060.34)/(6 - 4) = 15.72

Therefore, the intervals should be ordered from greatest to least average rate of change as follows:

1. Interval 12-10
2. Interval 8-6
3. Interval 14-12
4. Interval 10-8
5. Interval 6-4