Water flows over a dam at a rate of 500 gallons per minute. Write a function rule relating the amount of water (A) that flows over the dam to the number of minutes (M) that have passed. What are the initial value and rate of change?
The function rule relating the amount of water (A) that flows over the dam to the number of minutes (M) that have passed can be expressed as:
A = 500M
In this equation, M represents the number of minutes that have passed, and A represents the amount of water that has flowed over the dam.
The initial value (also known as the y-intercept) is zero because when M is zero (at the start), no time has passed, so no water has flowed over the dam yet.
The rate of change, or slope, in this case, is 500. This means that for every minute that passes, 500 gallons of water flow over the dam.
To write a function rule relating the amount of water (A) that flows over the dam to the number of minutes (M) that have passed, we can use the formula for the rate of flow.
The rate of flow is given as 500 gallons per minute, meaning that for every minute that passes, 500 gallons of water flow over the dam.
To find the function rule, we can start with the initial value, which represents the amount of water that flows over the dam when no time has passed. In this case, if no time has passed, the amount of water flowing over the dam would be zero gallons. Therefore, the initial value is 0.
Since the rate of flow is constant at 500 gallons per minute, the rate of change in the amount of water (A) is also 500 gallons per minute.
Therefore, the function rule relating the amount of water (A) to the number of minutes (M) that have passed is:
A = 500M
where A is the amount of water in gallons and M is the number of minutes that have passed.
The initial value is 0 gallons, and the rate of change is 500 gallons per minute.