Rate of Change Formula Rate of Change Formula Rate of change means the variation of a quantity with respect to time. It is a mathematical concept, but used extensively in Physics and Chemistry. The simple rate of change formula is given underneath: Rate of change = [final value – initial value] / time The simplest example of rate of change is velocity. It is defined as the rate of change of an object’s position. Thus the formula for velocity is: Velocity = [final distance – initial distance] / time. Rate of change is defined explicitly in calculus. We can define two types of the rate of chance. 1.
Average rate of change
2.
Instantaneous rate of change
Average rate of change is the ratio of the variation in the value of a quantity to the time passed.
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We can define this for a mathematical function as the ratio of the variation in the y - value to the variation in the x - value for two separate points on the graph of that function. Indeed, it is the same as the slope of a curve. The average rate of change formula is: Average rate of change = change in y value / change in time. If the change in y value is y2 – y1 and the change in time is t2 – t1, average rate of change formula is: Average rate of change = (y2 – y1) / (t2 – t1). For instance, let the price of a quantity be $15 at present and suppose that its price was $10 three years ago. Then the average rate of change is: Average rate of change = ($15 - $10)/3 = $5/3 per year. Instantaneous rate of change is calculated at a precise instant of time. The value of the instantaneous rate of change is identical to the value of the derivative at a specific point. We can describe the instantaneous rate of change at a specific point for a mathematical function as the slope of the tangent to a curve at that point. Jot down that when the intervals of time are relatively small, the average rate of change is roughly equivalent to the instantaneous rate of change. The instantaneous rate of change formula is: Instantaneous rate of change = small change in value/ small change in time. If we are calculating the instantaneous rate of change for a mathematical function, we represent it in the terms of the derivatives as: Instantaneous rate of change = d (f (a)) / d t.
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Here, f (a) is the function with variable ‘a’ and d (f (a)) / d t is the derivative of the function with respect to time. For instance, let us consider that we want to calculate the instantaneous rate of change for a curve f (a) = a2 + 3a +1 at point a = 4. Firstly, we will differentiate both sides of the equation. => f’ (a) = 2a + 3. Here, f’ (a) is the first derivative of the function f (a). The next step is to put in the value of the point, i.e. a = 4 in our derivative. => f’ (4) = 2 * 4 + 3. => f’ (4) = 11. Hence the instantaneous rate of change for the curve f (a) = a2 + 3a +1 at point a = 4 is 11.
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