water flows over a dam at a rate of 500 gallons per minute write a function rule relating the amount of water a that flow over the dam to the number of minutes m that have passed what are the initial value and rate of change
gals = (gals/min)(min)
a = 500m
To write a function rule relating the amount of water that flows over the dam to the number of minutes that have passed, we need to determine how the amount of water changes with time (in minutes).
Let's denote the amount of water that flows over the dam as "A" and the number of minutes that have passed as "m".
From the given information, we know that water flows over the dam at a rate of 500 gallons per minute. This means that for each minute that passes, 500 gallons of water flow over the dam.
Therefore, we can write the function rule as:
A = 500m
In this equation, "A" represents the amount of water in gallons and "m" represents the number of minutes. The function rule states that the amount of water, A, is equal to 500 times the number of minutes, m.
For example, if 10 minutes have passed, we can substitute m = 10 into the equation to find the amount of water that has flowed over the dam:
A = 500 * 10 = 5000 gallons
The initial value of the amount of water is when no time has passed, which is represented by m=0. Substituting m = 0 into the equation:
A = 500 * 0 = 0 gallons
Hence, the initial value is 0 gallons.
The rate of change is the coefficient of m in the equation, which is 500. This means that for every additional minute that passes, the amount of water flowing over the dam increases by 500 gallons.