The value of y changes by 3 units when x changes by 0.1 unit. About how fast is y changing?
Δy / Δx = 3/0.1 = 30 units
The average rate of change of y with respect to x is
Δy / Δx
=3/0.1
=?
To find how fast y is changing, we need to determine the rate of change, which is also known as the derivative. The question states that y changes by 3 units when x changes by 0.1 unit.
The rate of change is calculated by taking the difference in y divided by the difference in x. In this case, the rate of change is:
rate of change = (change in y) / (change in x)
So, plugging in the given values, we have:
rate of change = 3 units / 0.1 unit
Simplifying:
rate of change = 30 units per unit
Therefore, y is changing at a rate of 30 units per unit (or 30 units per 1 unit change in x).