To find the rate of change in terms of balance (in dollars) with respect to the number of weeks, we will calculate the change in balance over the change in weeks for the data provided.
We can use the formula for rate of change:
\[ \text{Rate of Change} = \frac{\text{Change in Balance}}{\text{Change in Weeks}} \]
We will calculate the change in balance and change in weeks between two points. We can take the first and last points for a larger interval:
- Starting point: Week 0, Balance 32
- Ending point: Week 13, Balance 123
Now, calculate the change in balance and the change in weeks:
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Change in balance: \[ \text{Balance at Week 13} - \text{Balance at Week 0} = 123 - 32 = 91 \text{ dollars} \]
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Change in weeks: \[ \text{Weeks at 13} - \text{Weeks at 0} = 13 - 0 = 13 \text{ weeks} \]
Now compute the rate of change:
\[ \text{Rate of Change} = \frac{91 \text{ dollars}}{13 \text{ weeks}} \approx 7 \text{ dollars per week} \]
Thus, the rate of change in terms of balance with respect to the number of weeks is approximately 7 dollars per week.