The value of y changes by 3 units when x changes by 0.1 unit. About how fast is y changing?

The average rate of change of y with respect to x is

Δy / Δx
=3/0.1
=?

300

Δy / Δx = 3/0.1 = 30 units

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).