Determine the initial value and the rate of change in the following description. A 2,000-gallon tank is half full with 1,000 gallons of water. Water is being pumped into the tank at a rate of 15 gallons per minute.(1 point)
The initial value is b=
, and the rate of change is m=
.
The initial value is b = 1,000 gallons, and the rate of change is m = 15 gallons per minute.
To determine the initial value and the rate of change in this description, we can use the equation of a line, which is y = mx + b, where y is the value being measured, x is the independent variable (in this case, time), m is the rate of change, and b is the initial value.
In this case, the value being measured is the amount of water in the tank (y), and the independent variable is time (x).
Given that the tank is half full with 1,000 gallons of water and water is being pumped into the tank at a rate of 15 gallons per minute, we can determine the values of b and m.
The initial value (b) is the starting point or the y-intercept. Since the tank is half full with 1,000 gallons of water when the pump starts, the initial value is b = 1000.
The rate of change (m) is how much the value (the amount of water in the tank) increases or decreases with respect to time. We are told that water is being pumped into the tank at a rate of 15 gallons per minute, so the rate of change is m = 15.
Therefore, the initial value (b) is 1000 gallons and the rate of change (m) is 15 gallons per minute.
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The initial value, b, in this description is 1,000 gallons because the tank is initially half full with 1,000 gallons of water.
The rate of change, m, is 15 gallons per minute because water is being pumped into the tank at a rate of 15 gallons per minute.