Question

A cockroach population doubles every three days. If there were c cockroaches on June 1st, what was the percent increase in the population on July 1st?

1) 900
2) 1,000

Answer 1

To find the percent increase in cockroach population, which doubles every three days, over a 30-day period, we calculate the number of times it doubles in that time (10 times) and use the formula for percent increase. The increase works out to a percent change of 102,300%, with the closest answer choice being 1,000%.

Step-by-step explanation:

The concept being asked about relates to exponential growth, which in this case applies to a population of cockroaches that doubles every three days. To find the percent increase over 30 days (from June 1 to July 1), we need to calculate the number of times the population doubles within this time period.

There are 10 three-day periods in 30 days. Because the population doubles every three days, over 30 days, it would double 10 times. If we let c be the initial number of cockroaches, the population on July 1st would be c × (2^10), which equals c × 1024. The percent increase is: ((Final population - Initial population) / Initial population) × 100%, which is ((c × 1024 - c) / c) × 100% = (1024 - 1) × 100% = 102300% increase.

So, the correct answer is (2) 1,000 (but more precisely, it should be 102,300% as a percent increase).