Question

use the graph to answer the following questions.
julies savings account

a. how much money did julie deposit into her savings account?

b. at what rate, in dollars per week, was julie adding money to her savings account in the first four weeks?

c. describe the slope for segment b? segment a? segment c?

d. which describes segment b?

Explanation:

Part a: How much money did Julie deposit into her savings account?

Step1: Identify the initial balance

From the graph, at time \( t = 0 \) (week 0), the balance is \( 100 \) dollars (the y - intercept of the graph).

Step2: Determine the deposit

The deposit is the initial amount she put into the account, which is the balance at week 0. So Julie deposited \( 100 \) dollars into her savings account.

Step1: Find two points on Segment A

Let's assume at \( t = 0 \) (week 0), the balance \( y_0=100 \) dollars. From the graph, at \( t = 4 \) weeks, let's assume the balance (from the grid) is \( y_4 = 300 \) dollars (since the graph goes up to 300 at week 4 for segment A).

Step2: Calculate the rate (slope)

The rate of change (slope) is given by the formula \( \text{Rate}=\frac{y_2 - y_1}{t_2 - t_1} \). Here, \( y_1 = 100 \), \( t_1 = 0 \), \( y_2=300 \), \( t_2 = 4 \). So \( \text{Rate}=\frac{300 - 100}{4 - 0}=\frac{200}{4}=50 \) dollars per week.

Step1: Analyze the direction of Segment A

Segment A is increasing (from left to right, the balance is increasing as time increases). The slope of an increasing line is positive.

Step2: Calculate the slope (from part b we know it's 50, which is positive)

So the slope of Segment A is positive (and has a value of 50 dollars per week as calculated earlier).

Answer:

\( 100 \) dollars

Part b: At what rate, in dollars per week, was Julie adding money to her savings account in the first four weeks?