Explanation

The percent increase is the difference between the amounts divided by the original, converted to a percent. If the population doubles, mathematically the increase can be written as a
power of 2. In the 30-day interval, if the original population is 1, it will double to 2 after three days —so, 21 represents the population after the first increase, the second increase would then be 22 and so on. Since there are 10 increases, the final population would be 210 or 1,024. Therefore, the difference, 1,024 – 1, is 1,023. Use the percent change formula to calculate percent increase:

Percent Change=$(\frac{Difference}{original} \times 100)$
Percent Change=$(\frac{1023}{1} \times 100)=102300 \%$

Note that the new number is 102,400% of the original, but that was not the question asked—the percent increase is 102,300%.