Finding the rate of change of the balance of a student's savings account.

To determine the rate of change of the balance of the student's savings account in dollars and cents per week, we need to calculate the slope of the line that represents the relationship between the week number and the balance. The rate of change (or slope) of a linear relationship is given by the formula: \[ \text{Slope} = \frac{\Delta y}{\Delta x} = \frac{\text{Change in balance}}{\text{Change in weeks}} \] We will use the data points provided in the table to calculate the slope. Let's choose two points from the table to find the slope. We'll use the points for Week 0 and Week 1: - Week 0, Balance: 32 dollars - Week 1, Balance: 39 dollars Now, we compute the change in balance and the change in weeks: \[ \text{Change in balance} = 39 - 32 = 7 \text{ dollars} \] \[ \text{Change in weeks} = 1 - 0 = 1 \text{ week} \] Using the slope formula: \[ \text{Slope} = \frac{7 \text{ dollars}}{1 \text{ week}} = 7 \text{ dollars per week} \] For confirmation and to ensure consistency, we can calculate using another set of points, for instance, Week 0 and Week 6: - Week 0, Balance: 32 dollars - Week 6, Balance: 74 dollars \[ \text{Change in balance} = 74 - 32 = 42 \text{ dollars} \] \[ \text{Change in weeks} = 6 - 0 = 6 \text{ weeks} \] Using the slope formula again: \[ \text{Slope} = \frac{42 \text{ dollars}}{6 \text{ weeks}} = 7 \text{ dollars per week} \] Since the rate of change is consistent regardless of the points chosen, the rate of change of the balance of the student’s savings account is: \[ 7 \text{ dollars per week} \] Thus, the rate of change of the balance of the student’s savings account is **7 dollars per week**.