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How do you determine if a rate of change is constant?
You can determine if a rate of change is constant, by taking the instantaneous rate of change at multiple points - if they are all equal to each other, it can be assumed that the rate of change is constant. Alternatively, you can differentiate the function (if there is an associated function) - if this comes to a constant i.e. a number, then the rate of change is constant.
How do you find rate of change if change is not constant?
Find the derivative
What is differential equations as it relates to algebra?
It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.
What is the unit rate of change of d with respect to t ( That is a change of 1 unit in t will correspond to a change of how many units in d )?
The unit rate of change of d with respect to t is the slope of the line representing the relationship between d and t. It indicates how much d changes for every one unit change in t. Mathematically, it is calculated as the change in d divided by the change in t, often denoted as Δd/Δt. This value represents the instantaneous rate of change at a specific point on the curve.
How do you determine the instantaneous rate of change of compound interest compounded annually?
The derivative is at*ln(a) wheret is the time period, ln is the natural log and a is the multiplier for the annual interest rate: eg if the interest rate is r% then a = (1 + r/100).
