Two-Variable Data: Models and Scatterplots

SAT Math· difficulty 4/5

A bacterial colony triples in size each day starting at 100 cells. After how many days will it exceed 8000 cells?

  • A

    4 days

  • B

    3 days

  • C

    5 days

    check_circle
  • D

    6 days

Explanation

100×3t>80003t>80100 \times 3^t > 8000 \Rightarrow 3^t > 80. 34=81>803^4=81 > 80, so t=5t = 5 days (since after 4 days = 8100, on day 5 still over). Wait, let me redo: day 1 = 300, day 2 = 900, day 3 = 2700, day 4 = 8100, day 5 = 24300. Exceeds 8000 first at day 4. Actually on day 4: 8100 > 8000 yes. So 4 days. Let me re-examine: After 4 days = 10034=8100100 \cdot 3^4 = 8100. So answer is 4 days.

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