The difference between a geometric sequence and an exponential function?

Geometric sequences and exponential functions are very closely related. As a result, geometric sequences and exponential functions look very similar. The fundamental difference between the two concepts is that a geometric sequence is discrete while an exponential function is continuous.

The relation between speed, distance and time can be illustrated using the following rule:
speed = distance / time
This means that to get the distance traveled at a certain speed through a given interval of time, all we have to do is multiply the speed by the time.
i.e.
distance = speed * time

Now, if the time is constant, we can note that as the speed increases the distance traveled increases and vice versa.

This means that at constant time, the speed and the distance are directly proportional to each other.

Hope this helps :)