Question

jina has been withdrawing the same amount of money from account every month. the table below shows the amount of account after different amounts of time.
time (months) 6 8 10 12
money (dollars) 460 330 200 70
answer the following questions.
(a) choose the statement that best describes how the time and the amount of money in her account are related. then give the value requested.
○ as time increases, the amount of money in her account decreases.
at what rate is the amount of money in her account decreasing?
□ dollars per month
○ as time increases, the amount of money in her account increases.
at what rate is the amount of money in her account increasing?
□ dollars per month
(b) how much money was in her bank account before jina started withdrawing money?
□ dollars

Explanation:

Step1: Identify relationship direction

From the table, as time (months) goes from 6 to 12, money drops from 460 to 70, so money decreases with time.

Step2: Calculate monthly decrease rate

Pick two points, e.g., (6, 460) and (8, 330). Compute rate: $\frac{460 - 330}{8 - 6} = \frac{130}{2} = 65$ dollars per month.

Step3: Find initial account amount

Use linear equation $y = -65x + b$, plug in $x=6, y=460$.
$460 = -65(6) + b$
$460 = -390 + b$
$b = 460 + 390 = 850$

Answer:

(a)

• Chosen statement: As time increases, the amount of money in her account decreases.
• Rate: 65 dollars per month

(b) 850 dollars