Originally Posted by

**otownsend** Hello,

I have the two equations:

h(x) = 3(3)^x

f(x) = 100(2)^(x/32)

*h(x)* is the number of people told during the hour, x, and x = 0, corresponds to the hour which the first 3 people heard the rumour and started telling others.

*f(x)* is the total number of bacteria within a culture which doubles every 0.32 hours, and *x* is the number of hours. x = 0 corresponds to the initial amount of bacteria (which is 100).

**This is the dilemma that I am having. **Both equations are very similar, and yet, h(x) represents the *total additional amount* of people told based on the number of hours since the beginning and f(x) represents the *total amount* of bacteria based on the number of hours since the beginning.

**Is there any fundamental reason why one represents the total amount versus another only represents the total additional amount? I'm having a hard time wrapping my head around this. I did not create these equations. I feel like it is important for me to understand the difference in order to be able in the future to derive equations which represent the context of the situation correctly. **