What is algebra? why does algebra used for?

On a piece of paper graph f(x)=5•(0.4)^x

10 ! a train starts from grand city and travels toward belleville 388 miles away. at the same time, a train starts from belleville and runs at the rate of 47 miles per hour toward grand city. they pass each other 4 hours later. find the rate of the train from grand city.

These tables represent a quadratic function with a vertex at (0, -1). what is the average rate of change for the interval from x = 9 to x = 10?