Advanced MathEasy–MediumInterpreting the base of an exponential model
Advanced Math practice question
The population of a town t years after 2020 is modelled by P(t) = 500(1.04)^t.
What does the number 1.04 indicate about the population?
- A. It increases by 4% each year.Correct
- B. It increases by 104% each year.
- C. It increases by 4 people each year.
- D. It decreases by 4% each year.
Answer: A. It increases by 4% each year.
In P(t) = 500(1.04)^t, each year multiplies the population by 1.04 — that is, by 100% + 4%. Multiplying by 1.04 is the same as adding 4% of the current value, so the population grows by 4% per year.
Why the other answers are wrong
- B. It increases by 104% each year.
- A 104% increase would multiply by 2.04, not 1.04. The '1' in 1.04 is the existing 100%; only the .04 is the increase.
- C. It increases by 4 people each year.
- Multiplying by 1.04 adds 4% of the CURRENT population, not a fixed 4 people. A fixed yearly addition would be a linear model, P(t) = 500 + 4t.
- D. It decreases by 4% each year.
- A base greater than 1 means growth. Decay by 4% per year would use the base 0.96.
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