Question

vanessa opens a new savings account. she makes an initial deposit, and then deposits the same amount each week. the total number of dollars in the account, y, is a function of the number of weeks, x. initial value: 10 is the rate of change positive or negative? positive how can you find the rate of change? rate of change =? /? number of weeks, x | amount saved, y 0 | 10 1 | 15 2 | 20 3 | 25

Explanation:

Step1: Recall the formula for rate of change

The formula for rate of change (slope) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Choose two points from the table

Let's take the points \((x_1 = 0,y_1=10)\) and \((x_2 = 1,y_2 = 15)\).

Step3: Calculate the rate of change

Substitute into the formula: \(m=\frac{15 - 10}{1 - 0}=\frac{5}{1}\).

Answer:

rate of change \(=\frac{\text{change in }y}{\text{change in }x}\)