GED Mathematical Reasoning TestQuantitative Problem Solving with Rational NumbersHard
A biologist is observing a bacterial culture. The population started with 400 bacteria and increased by 30% every hour for 3 hours. What was the approximate bacterial population after 3 hours?
- A1200
- B1040
- C913
- D520
Show answer & explanationAnswer & explanation
Correct answer: C. 913
To find the population after 3 hours, we apply a 30% increase for each hour. This involves calculating 130% (1.30) of the previous hour's population iteratively. The final calculation shows an approximate population of 913.
Why the other options are wrong
- A. This is a result of incorrectly adding 30% of the initial population three times, rather than compounding the growth.
- B. This might be a result of incorrectly calculating the increase or only doing two steps.
- D. This is the population after 1 hour, not 3 hours.
Compound Percentage Growth
Compound percentage growth occurs when an initial quantity increases by a certain percentage, and then the new total increases by that same percentage in subsequent periods, leading to exponential growth.
- Growth is applied to the new total each period.
- Can be calculated using the formula P * (1 + r)^n, where P is initial, r is rate, n is periods.
- Results in a larger total increase than simple interest over time.
Memory trick: Grow, then grow on the new 'glow'.