JoAnne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months, there is $300 in the account. Find the constant rate of change of the account.
(300-150)/(6-3) = $50/mo
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To find the constant rate of change, we need to determine how much the account balance increases per month.
Let's assume that the initial amount JoAnne deposited is represented by "a" and the constant rate of change is represented by "r".
After 3 months, the account balance is $150, so we can write the equation:
a + 3r = 150
After 6 months, the account balance is $300, so we can write the equation:
a + 6r = 300
To find the constant rate of change (r), we can solve these two equations as a system of linear equations.
Here's how we can do that:
1. Multiply the first equation by 2 to eliminate "a".
2(a + 3r) = 2(150)
2a + 6r = 300
2. Subtract the second equation from the result to eliminate "a".
(2a + 6r) - (a + 6r) = 300 - 300
a = 0
3. Substitute the value of "a" into either equation to solve for "r".
a + 3r = 150
0 + 3r = 150
3r = 150
r = 50
Therefore, the constant rate of change is $50 per month.
To find the constant rate of change of the account, we can use the formula for the slope of a line, which is the change in the y-values divided by the change in the x-values.
Let's assign variables to the time and account balance. Let t represent the number of months and b represent the account balance.
We can set up two equations using the information given:
When t = 3, b = $150
When t = 6, b = $300
Using these two points, we can calculate the constant rate of change.
First, let's find the change in the account balance (Δb) over the change in time (Δt):
Δb = $300 - $150 = $150
Δt = 6 - 3 = 3
Now we can calculate the constant rate of change (slope) using the formula:
slope = Δb / Δt = $150 / 3 = $50 per month
Therefore, the constant rate of change of the account is $50 per month.