- The rate at which the amount of money in the account is increasing is 45 dollars per month.
- The initial amount of money in Tammy's account is equal to $197.
How to determine the relationship between the time and the amount of money?
In order to determine the relationship between the time and the amount of money in the account, we would calculate the average rate of change.
What is the average rate of change?
The average rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
Mathematically, the slope (average rate of change) can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
For Tammy's account, we have:
Points (x, y) = (6, 467) (8, 557)
Average rate of change = (557 - 467)/(8 - 6)
Average rate of change = 90/2
Average rate of change = 45.
As time increases, the amount of money in Tammy's account increases. Also, the rate at which the amount of money in the account is increasing is 45 dollars per month.
How to determine the initial amount?
First of all, we would determine the increment in 6 months as follows:
Increment = $45 × 6
Increment = $270.
Initial amount = $467 - $270
Initial amount of money = $197.
Read more on average rate of change here: https://brainly.com/question/19732795
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