Advanced MathMediumInterpreting a decay factor
Advanced Math practice question
The population of a village t years from now is modelled by P(t) = 1200(0.97)ᵗ.
Which of the following best describes how the population changes from one year to the next?
- A. It decreases by 3%.Correct
- B. It decreases by 97%.
- C. It decreases by 3 people.
- D. It increases by 3%.
Answer: A. It decreases by 3%.
Each year multiplies the population by 0.97, which is 97% of the previous value. Keeping 97% means losing 3%.
Why the other answers are wrong
- B. It decreases by 97%.
- Multiplying by 0.97 KEEPS 97%; the loss is the other 3%.
- C. It decreases by 3 people.
- The change is a percentage of the current population, not a fixed number of people. Losing 3 people each year would be P(t) = 1200 − 3t.
- D. It increases by 3%.
- A base less than 1 means decrease. Growth of 3% would use 1.03.
More Advanced Math questions
- Medium
What are the solutions to x² − 5x + 6 = 0? - Medium
The graph of f(x) = (x − 3)² + 4 is a parabola. What are the coordinates of its vertex? - Medium
If x² − 2x − 8 = (x + 2)(x − a), what is the value of a? - Medium
If √(x + 5) = 4, what is the value of x? - Medium
If f(x) = x + 3 and g(x) = 2x, what is f(g(4))? - Medium
What are the solutions to x² + 6x + 8 = 0?
Not affiliated with the College Board. SAT is a trademark of the College Board.