The rate of change is a measure of how much a quantity changes as another quantity changes. In this exercise, we are concerned with how quickly luminous intensity increases as voltage changes. To determine this, we use the derivative of the intensity function:
- \(\frac{dI}{dV} = 10^{-3} V\)
This represents the rate of change of luminous intensity with respect to voltage.
The given problem asks us to find the voltage at which this rate of change is 0.4 candelas per volt. By setting the derivative equal to the desired rate (0.4 candelas/volt), we solve for the voltage, finding that:
Understanding rates of change is vital in many real-world applications, as it helps predict how systems will react under various conditions. It's particularly useful in fields that require precise control and optimization, such as engineering and physics.