Advanced MathMediumIdentifying the function from a description of growth
Advanced Math practice question
A quantity starts at 80 and decreases by 25% each year. Which function gives the quantity Q after t years?
- A. Q(t) = 80(0.75)ᵗCorrect
- B. Q(t) = 80(0.25)ᵗ
- C. Q(t) = 80 − 20t
- D. Q(t) = 80(1.25)ᵗ
Answer: A. Q(t) = 80(0.75)ᵗ
A 25% decrease each year keeps 75%: multiply by 0.75 each year.
Why the other answers are wrong
- B. Q(t) = 80(0.25)ᵗ
- 0.25 keeps only a quarter, a 75% decrease.
- C. Q(t) = 80 − 20t
- 80 − 20t subtracts 25% of the ORIGINAL each year (linear), not of the current value.
- D. Q(t) = 80(1.25)ᵗ
- 1.25 is a 25% increase.
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