Why do businesses care about rate(s) of change?
In economics, a firm wants to maximize profit. Your ice cream shop has some costs that vary depending on how many half-gallon ice cream packages are made, and some benefits, the revenue from selling ice cream. The additional cost of making one more package of ice cream is called the marginal cost, and it can change based on how much ice cream you are already making. The marginal benefit of course the price that you sell each package for.

In order to maximize profit, you have to choose some quantity of ice cream packages to produce. You do this by setting marginal cost equal to marginal benefit, and then solving for production. So if you have a formula for what the price of ice cream will be over time, then you can predict your marginal benefit  of production over time, and can anticipate what your production will look like in the future.