Question

ashley deposits the same amount of money into a bank account every month. the table below shows the amount of money in the account after different amounts of time.
time (months) | 6 | 8 | 10 | 12
money (dollars) | 467 | 557 | 647 | 737
answer the following questions.
(a) how much money was already in the account when ashley started depositing money?
dollars
(b) choose the statement that best describes how the time and the amount of money in the account are related. then give the value requested.
○ as time increases, the amount of money in the account decreases.
at what rate is the amount of money in the account decreasing?
dollars per month
○ as time increases, the amount of money in the account increases.
at what rate is the amount of money in the account increasing?
dollars per month

Explanation:

Step1: Find the rate of change (slope)

The table has time (x) and money (y) values: (6, 467), (8, 557), (10, 647), (12, 737). Let's take two points, say (6, 467) and (8, 557). The slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{557 - 467}{8 - 6} = \frac{90}{2} = 45 \). So the rate of increase is 45 dollars per month.

Step2: Find the initial amount (y-intercept)

Use the slope-intercept form \( y = mx + b \). Plug in \( x = 6 \), \( y = 467 \), and \( m = 45 \): \( 467 = 45(6) + b \). Calculate \( 45(6) = 270 \). Then \( b = 467 - 270 = 197 \). So the initial amount is 197 dollars.

Step3: Analyze the relationship

As time (months) increases, the money in the account increases (since slope is positive 45).

Answer:

(a) 197
(b) As time increases, the amount of money in the account increases.
At what rate is the amount of money in the account increasing? 45 dollars per month