Question

Which situations can be represented by an exponential function?

1) An event organizer finds each year's attendance for the past five years is about 45% of the previous year's attendance.
2) An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.
3) A toad population is increasing by about 7.5%.

Answer 1

Situations 1 and 2 are cases of exponential decay, where attendance decreases by a constant percentage each year, while situation 3 is a case of exponential growth, with a toad population increasing by a fixed percentage over time.

Step-by-step explanation:

The situations that can be represented by an exponential function are those where a quantity increases by a constant percentage or fraction at each step. In the case of situation 1, where an event's attendance is 45% of the previous year, this is a case of exponential decay, which is the inverse of exponential growth, as the quantity is decreasing by a percentage each time. Situation 2 also represents exponential decay, since the attendance each year is 4/5 of the previous year's, indicating a constant proportional decrease. Lastly, situation 3, where a toad population is increasing by about 7.5% each period, is a classic example of exponential growth, where the population size increases by a constant percentage over time.