Question

amy and daniel compared the balances of their saving accounts each month during the first half of the year. the graphs generated from this data are shown below.
what can be concluded from the graph?
a. at the beginning of the year, the balance in daniels account was three times the balance in amys account.
b. at the beginning of the year, the balance in amys account was three times the balance in daniels account.
c. during the first half of the year, amys account balance grew three times as fast as daniels balance.
d. during the first half of the year, daniels account balance grew three times

Explanation:

Step1: Determine the initial balances

At month \(0\) (beginning of the year), the balance in Daniel's account is \(0\) and the balance in Amy's account is also \(0\). So options A and B are incorrect.

Step2: Calculate the rate of growth (slope)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For Daniel's account: Let \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(6,540)\). Then \(m_{Daniel}=\frac{540 - 0}{6-0}=90\).
For Amy's account: Let \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(6,180)\). Then \(m_{Amy}=\frac{180 - 0}{6 - 0}=30\).
Since \(m_{Daniel}=3\times m_{Amy}\), Daniel's account balance grew three times as fast as Amy's balance.

Answer:

D. During the first half of the year, Daniel's account balance grew three times as fast as Amy's balance.