Um, no, exponential doesn’t have to be doubled or tripled. Exponential growth means that the amount of growth is directly proportional to the current value.
Compound interest: interest earned is a percentage of current balance. Yep.
Population growth: the more people there are, the more births can happen. Yep.

This is not entirely correct. You’re right that exponential growth means doubling (or any multiplier) and not just regular growth, however most of these things are still examples of exponential growth. Exponential growth occurs when the rate of change depends on the value of the variable at that point, that is f'(x) = kf(x). Exponential functions like f(x) = 2^x are examples of this since f'(x) = Ln(2) 2^x .

In English take the example of cancer cells. One cancer cell can make another, and that pair can now make another pair, and quartet can make another quartet. The amount of NEW cells depends on how many cells there are at any moment. That is exponential growth.

I think Cancer, Pandemics and Epidemics, Water Hyacinths and Population come under doubling, Cancer divides upon binary fission, same for most epidemics and pandemics and Water Hyacinths and Population exhibit J curves like that of exponential growth graphs, but the rest of them are just ordinary growth