16Hit1600
Advanced MathMediumModel for a quantity that doubles every 6 hours

Advanced Math practice question

A culture of yeast cells doubles in size every 6 hours. If it starts with 5 million cells, which function gives the number of cells N(t), in millions, after t hours?

  1. A. N(t) = 5 · 2^(t/6)Correct
  2. B. N(t) = 5 · 2^(6t)
  3. C. N(t) = 5 · 6^t
  4. D. N(t) = 5 + 2t/6

Answer: A. N(t) = 5 · 2^(t/6)

Each 6-hour period doubles the count, and t hours contain t/6 such periods: 5 · 2^(t/6). Check: at t = 12, 5 · 2² = 20.

Why the other answers are wrong

B. N(t) = 5 · 2^(6t)
2^(6t) doubles six times every hour, far too fast; it should double once every 6 hours.
C. N(t) = 5 · 6^t
6^t multiplies by 6 every hour; the growth factor is 2, per 6 hours.
D. N(t) = 5 + 2t/6
5 + 2t/6 grows by a constant amount; doubling is exponential.

More Advanced Math questions

Not affiliated with the College Board. SAT is a trademark of the College Board.