GED Mathematical Reasoning TestQuantitative Problem Solving with Rational NumbersMedium
A biologist is studying a bacterial culture that initially contains 2.5 x 10^3 bacteria. The culture triples in size every hour. How many bacteria will be in the culture after 3 hours?
- A2.25 x 10^4
- B2.025 x 10^5
- C6.75 x 10^4
- D7.5 x 10^3
Show answer & explanationAnswer & explanation
Correct answer: C. 6.75 x 10^4
Initial bacteria = 2.5 x 10^3. After 1 hour, it triples: (2.5 x 10^3) * 3 = 7.5 x 10^3. After 2 hours, it triples again: (7.5 x 10^3) * 3 = 22.5 x 10^3 = 2.25 x 10^4. After 3 hours, it triples once more: (2.25 x 10^4) * 3 = 6.75 x 10^4.
Why the other options are wrong
- A. Incorrect. This is the amount after 2 hours.
- B. Incorrect. This would be the result if it tripled 4 times or if there was a calculation error.
- D. Incorrect. This is the amount after 1 hour.
Exponential Growth with Scientific Notation
Exponential growth occurs when a quantity increases by a constant factor over equal time intervals. When dealing with very large or small numbers, scientific notation is used to express them concisely.
- Initial amount multiplied by the growth factor raised to the power of time periods.
- Scientific notation expresses numbers as a coefficient times a power of 10.
- When multiplying numbers in scientific notation, multiply coefficients and add exponents.
- Adjust coefficient to be between 1 and 10, adjusting exponent of 10 accordingly.
Memory trick: Start with the base, multiply by the factor, for each time you pass.