The final type of Rate problem on the GRE is the Population problem. In such problems, some population typically increases by a common factor every time period. These can be solved with a Population chart.
Consider the following example:
The population of a certain type of bacterium triples every 10 minutes. If the population of a colony 20 minutes ago was 100, in approximately how many minutes from now will the bacteria population reach 24,000?
You can solve simple Population problems, such as this one, by using a Population chart. Make a table with a few rows, labeling one of the middle rows as “NOW.” Work forward, backward, or both (as necessary in the problem), obeying any conditions given in the problem statement about the rate of growth or decay. In this case, simply triple each population number as you move down a row. Notice that while the population increases by a constant factor, it does not increase by a constant amount each time period.
For this problem, the Population chart below shows that the bacterial population will reach 24,000 about 30 minutes from now.
In some cases, you might pick a Smart Number for a starting point in your Population chart. If you do so, pick a number that makes the computations as simple as possible.
| Time Elapsed | Population |
| 20 minutes ago | 100 |
| 10 minutes ago | 300 |
| NOW | 900 |
| in 10 minutes | 2,700 |
| in 20 minutes | 8,100 |
| in 30 minutes | 24,300 |
The population of amoebas in a colony doubles every two days. If there were 200 amoebas in the colony six days ago, how many amoebas will there be four days from now?