Advanced MathMediumInterpreting the base of an exponential model
Advanced Math practice question
The number of bacteria in a dish t hours after an experiment begins is modelled by N(t) = 1000(1.5)ᵗ. Which of the following is the best interpretation of the number 1.5?
- A. The population multiplies by 1.5 each hour — a 50% increase per hour.Correct
- B. The population increases by 1.5 bacteria each hour.
- C. The population increases by 1.5% each hour.
- D. There were 1.5 bacteria at the start.
Answer: A. The population multiplies by 1.5 each hour — a 50% increase per hour.
An exponential model's base is the hourly growth factor: 1.5 means 50% growth per hour.
Why the other answers are wrong
- B. The population increases by 1.5 bacteria each hour.
- 1.5 is a multiplier, not a count.
- C. The population increases by 1.5% each hour.
- 1.5% growth would be a base of 1.015.
- D. There were 1.5 bacteria at the start.
- The initial count is 1000.
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