ATI TEAS (Test of Essential Academic Skills) Version 7MathematicsHard
A researcher is charting the growth of a bacterial colony. The colony starts with 200 cells and increases by 15% every hour. Approximately how many cells will be in the colony after 3 hours?
- A290 cells
- B312 cells
- C304 cells
- D320 cells
Show answer & explanationAnswer & explanation
Correct answer: C. 304 cells
This is a compound growth problem. After 1 hour: 200 * (1 + 0.15) = 200 * 1.15 = 230 cells. After 2 hours: 230 * 1.15 = 264.5 cells. After 3 hours: 264.5 * 1.15 = 304.175 cells. Rounded to the nearest whole number, this is 304 cells.
Why the other options are wrong
- A. Incorrect; this might be a simple interest calculation (200 + 3*0.15*200 = 290).
- B. Incorrect; likely a miscalculation in the compound growth steps.
- D. Incorrect; significantly overestimates the growth.
Compound Percentage Growth
Growth where an initial amount increases by a fixed percentage over successive periods, with the percentage applied to the new, larger amount each time.
- Formula: Final Amount = Initial Amount * (1 + Rate)^Time.
- Rate must be in decimal form.
- Different from simple interest/growth.
Memory trick: Start Amount, Times (1 + Rate) to the Power of Time!