Advanced MathEasy–MediumWriting an exponential model
Advanced Math practice question
A bacteria culture starts with 200 cells, and the number of cells triples every hour. Which function gives the number of cells N(t) after t hours?
- A. N(t) = 200 · 3ᵗCorrect
- B. N(t) = 200 + 3t
- C. N(t) = 3 · 200ᵗ
- D. N(t) = 200 · t³
Answer: A. N(t) = 200 · 3ᵗ
Tripling every hour means multiplying by 3 once per hour: after t hours, by 3ᵗ. Starting from 200, that's 200 · 3ᵗ. Check: after 2 hours, 200 · 9 = 1,800.
Why the other answers are wrong
- B. N(t) = 200 + 3t
- 200 + 3t adds 3 cells per hour — linear growth. Tripling multiplies; it doesn't add a fixed amount.
- C. N(t) = 3 · 200ᵗ
- 3 · 200ᵗ raises the starting number to the power t. The base of the exponential is the growth factor, 3, and 200 is the starting value.
- D. N(t) = 200 · t³
- 200 · t³ cubes the time. Exponential growth puts t in the EXPONENT, not the base.
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