In that case, the rate of change changes all the time as well. In the following, I use the symbol "^" for powers. The derivative (rate of change) of the function:
2^x
is:
ln 2 times 2^x
(where ln 2 is the natural - base-e - logarithm of 2).
Chat with our AI personalities
To find the rate of change. Velocity, for example, is the rate of change of distance - in a specified direction. Acceleration is the rate of change of velocity.
The rate of change would be 1.5
For a line, the rate of change is the slope of a function.Example:y = 5x + 10The slope is 5. Every time x moves 1"unit", y moves 5 "units".The rate of change would be stated as rise / run. 5 units / 1 unit = 5
"Rate of change" means how quickly something changes. Examples in physics include a speed as a rate of change of position - if your position changes 10 meters every second, then that (10 meters/second) is your rate of change of position, or your velocity. Or if your income increases by a thousand dollars a year, then that's the rate of change of your income - how quickly your income changes.
Some examples: Your velocity is the rate of change of distance (even if you don't think of it in that way). Your acceleration is the rate of change of velocity. Your pay rise is the rate of change of your pay (per year).